It is currently not against the law to drive a car without spare tyre in the UK in the boot.
However, many people recommended that do keep one in your car if possible. If you experience a puncture having a spare tyre that you can fit in place of the broken tyre can help get you back on the road.
If you having a spare tyre in your boot, this also means you are able to fix the problem or a tyre failure yourself. At least temporarily until you can drive to a garage or get home. Instead of calling out a breakdown service or a friend to come and collect you.
Although it's not mandatory, many will advise that drivers to carry a spare wheel with them when travelling. Especially if you are driving over long distances or in remote locations.