Short term buying vs renting - which makes more sense

UPDATE: Thanks for the advice, all. I'm going to go with the rental option.

Hey all.

So I'll preface this by saying I'm dyscalculic so please make your advice as dumbed-down as possible as my brain just switches off when I see maths.

In approximately 5 months, I'll be moving house, my wife and I have amicably separated but due to finances she has allowed me to remain in our current house for free for basically as long as I need to. (I won't get into the details but basically it boils down to her being lovely - it's entirely her house and she owes me nothing). I said I'd stay for 7 months and then re-assess but obviously, the longer I stay here, the longer it will be before either of us can properly move on. This happened just over 2 months ago so I've got 5 months left.

In that time, I should be able to save up somewhere between £15-20k. It will most likely be closer to the £15k so let's say £20k is a stretch-goal.

My plan is to move from the South (Surrey) to the North (Leeds) as I have family and a few friends (admittedly these are lapsed friendships but I'm hoping to rekindle them) there.

As I'm in my 40's and am now single, I don't really want to be too far from the city centre as I'll end up isolating myself. So my plan was to either buy or rent a flat in the city for a few years (no longer than 3 years, ideally as I don't love living in flats but I can cope with it for that long) and then buy a house a bit further out, once I've re-established a decent life in Leeds.

My budget for buying would be around the £250k mark (assuming a 5% deposit). I'm assuming ~£2500 in stamp-duty and I have NO idea what to expect for solicitors fees.

My budget for renting would be around £1500/month (that's the sweet spot between having a nice place that I wouldn't hate and still having enough money left over to continue saving around £700-1000 a month for a higher deposit later). That's my max rent budget, obviously I'd rather pay less but I don't want to live somewhere I won't be happy.

My question is this (tl:dr):

At what point does it make more financial sense to just rent the flat instead of buying it? Is 2-3 years enough time to actually have any benefit or will the up-front cost stop it from being worth it?