Big dumb question, but let's say UBI did come into action and we all got £2k a month. Wouldn't everything just cost correct to make the £2k worth nothing?
Kinda like a mini hyper inflation? Renting would just start at 2k + whatever the normal figure is now? Stuff like that?
That depends on a lot of things.
The way to think about inflation is this: if you have more money chasing the same amount of stuff, you'll get inflation. You can see this happen in a lot of places; the one that always springs to mind for me is Somalia. When pirates started hijacking cargo ships and getting bounties for hundreds of thousands of dollars paid, the prices for local food and other supplies went through the roof. So, same amount of stuff with more money means inflation.
You can also see this in some rental markets like SF or London. SF is a prime example: they have restrictive planning laws so housing supply is short. Lots of techbro millionaires come flooding in and prices go through the roof.
However, if someone gets more money and they are able to buy things they otherwise wouldn't, there's no inflation. Instead that's just a straight increase in consumption. For most people on low incomes, they have lots of unmet needs that they would spend that money on. So, you can see how in reality you get both real growth and inflation when people have more money in their pocket.
So, to answer your question, the answer is
maybe. In places like London where the rental market is broken, then yes there's a good chance that any extra money would just get eaten up by landlords. They would know everyone has got more money and just put the prices up. This is one of the big problems with UBI: it's not a solution by itself. In the USA, there's a good chance that any UBI would also get eaten up by health insurance premiums.
UBI is only part of the solution. What's also needed is for things where supply is constrained and demand is inelastic - such as housing and healthcare - to either be regulated, or decommodified and provided on the basis of need. That's the only way to ensure that UBI is spent on real need and not just subsidising rent seeking behaviour.