Welcome to the Orchid Board! Congratulations on choosing a beautiful orchid that is easy to grow and flower in your climate.
It is likely a Dendrobium nobile hybrid as aliceinwl said. The species name is pronounced "NO-bee-lay." These are hybrids of related southeast Asian species from areas with humid, wet summers, and cool dry winters. They have a particular life cycle and watering requirements, including very heavy watering while making active growth in spring/summer.
You will get many opinions from orchid growers. I think the roots and potting mix look fine, and I would not repot your plant until next spring. Most beginners have trouble watering this plant enough. I think moving it to a medium that dries out faster is not a good idea, unless you want to water every day.
This kind of Dendrobium is often winter deciduous, but that is not required. After a cool and somewhat dry winter, it normally flowers in late winter. Then it begins growing new shoots from the base in spring. Your watering through the winter did not hurt it, but next winter it would be better to water only very occasionally, just enough to keep leaves from flagging. If you kept it at room temperature through the winter, that likely kept it from flowering this spring.
When you water, take it out of the decorative pot. Water the plant well, then let it drain for 10-30 minutes before returning it to the decorative pot. You don't want it standing in water.
It is beginning new growth. Let it dry somewhat before watering again as growth starts, but don't let it get bone dry. Check the moisture in the pot by inserting a wooden cooking skewer for a few minutes, then withdrawing and inspecting for moisture.
As it forms more new shoots from the base, and they lengthen, it will need more and more water. Don't let it dry out at this stage. The commonest problem I see with this kind of plant is people don't water enough during active growth, and they stunt the plant. It makes a large number of thin leaves that flag when thirsty.
Shoots (canes, stems) live for several years, even leafless. Don't cut them off until they turn brown and die. Sometimes they surprise you with flowers.
Keep it brightly lit. In England it could be in the sunniest spot, even outdoors for the summer.
When in growth, keep it well fertilized. Yamamoto Dendrobiums recommends lower nitrogen fertilizer. They say not to use sustained-release fertilizers because they persist too late in the summer, and prevent flowering. In my experience here in a warm climate where they grow for a very long time each year, commonly sold formulations with macronutrients around 20-20-20 with micronutrients work well. In your shorter growing season maybe it makes sense to use a lower nitrogen fertilizer less often than I use it.
I'm not familiar with English cooking measures, but a US Tablespoon holds 15ml. I use 1 Tablespoon per gallon of 20-20-20 with micronutriets for mine. You might want to use a smaller amount of fertilizer, like 1 teaspoon (5ml of powder.) For this kind of Dendrobium, starting now, and next year starting as soon as buds are formed and new shoots form at the base, you could fertilize every other watering. Because buds form at nodes on canes, longer growths will produce more flowers. Fertilizing maximizes cane length.
Stop fertilizing in mid to late August. Keep watering. The main reason they fail to flower is fertilizing too late in the year. If people fertilize too late the plant will form small plantlets along the canes instead of buds. These can be removed and grown on.
As fall progresses keep watering. With good care your new canes will be at least as long as the old ones. People stake them upright, or allow them to droop to the sides. As growth matures they need less watering. Water to keep leaves from flagging.
Despite common belief, they do not need to dry out and lose leaves in order to flower. Cool nights, 50 F / 10C or lower, are what triggers flowering. Commercial growers keep them cool, but continue watering. You can see this because they are sold in dense flower with full sets of leaves.
Try to keep as cool as you can through winter nights. You can let them get down near freezing. If frost is not expected where you live, they can spend winter days and nights outside. This will greatly enhance spring flowering. If you don't have outdoor space, you could keep the plant in a room with heat turned down, or keep it close to a window with the curtains drawn behind it. Don't let it freeze.
When flower buds appear along the canes in late winter, be sure it does not dry out. You can delay bud opening by keeping cool, or hasten by bringing into a warmer spot. Around the time of flowering they will begin making new shoots, and it will be time to begin fertilizing again.
You can repot any time during active growth. Best would be just after flowers fall. I would repot your plant in spring 2021 after flowering. Use a pot 2"-3" larger in diameter than the root ball. For tall plants, a wide heavy pot helps with toppling issues.
Many orchidists recommend bark for potting medium. Due to the very high water requirements of this kind of plant when in active growth, and the frequent requests for help to Orchid Board from people who have not watered their Dens enough, I think that it is fine to use high-quality, very loose potting soil. Or you could mix soil 50:50 with bark particles or large perlite. As I mentioned earlier, I would not use bark nor scoria for this kind of orchid unless you can water every day when it's in active growth.
Thin-leafed orchids are susceptible to spider mite attack during periods of warm, dry air. This manifests as unhealthy leaves with fine webbing underneath. The mites are almost microscopic in size, so you will probably not see them. If not treated they can kill the plant. They can be treated by spraying all plant surfaces, plus the surface of the potting medium, with 15ml liquid dish soap in a liter of water. The mites will come back so pay attention.
Yamamoto Dendrobuiums in Japan hybridizes and produces a great number of these plants. Their Web site formerly had excellent growing information for hobbyists. What I have written above is taken from that page, which I saved. Unfortunately it is no longer there. You can still look at the varieties they grow, and maybe see one very similar to yours.
They now have a
page showing how to force Dendrobium nobile for Christmas flowering in Japan's climate. There is a lot to learn from that page, but it is intended for growers who can artificially heat and cool their greenhouses during off seasons. Note they use coconut husk for growing medium, which many orchidists would say retains too much water for orchids. For many orchids that is correct, but not for this kind of very thirsty orchid.