The last time I was in Ireland, you'd still occasionally encounter a horse-drawn sulky on the roads. I've no idea if that is also the case in the UK, but a horse is more practical than an ox.
I can only speak of London - it is very rare to see oxes there. In fact, in my various visits to this city, I actually never saw an ox on the streets. In Oxford I would expect some, though. Oxford is in Oxfordshire - look how many ox-names there are. It's actually not so far away from London.
West Oxfordshire District Council is currently trying to find a way to stop a certain demographic from racing ponies and traps on the A40 dual carriageway.
Calling them travellers and/or gypsies (I know they are technically different groups of people but generally the terms are often used interchangeably) is not in itself a slur.