Isn't 80k miles a bit steep for a 1L 3 cylinder petrol?

Engine size has no impact on how reliable or otherwise an engine is (nor has the amount of cylinders), it is down to three things.

1, How well engineered it is (and in this respect, VAG seem to have got it right with the 1.0TSI*)

2, How well the car is looked after.

3, How the car is driven.

*There is a one owner (FSH) Seat Leon 1.0TSI on Autotrader right now with 163k miles. That is essentially the same engine (slightly more power) as the car I linked.

About 15k

Then a modern petrol engined car is still well worth going for, as most 'ordinary' ones can achieve a real-world mpg well in excess of 40 average, and often in excess of 50 on longer runs on fast flowing roads like motorways.

In addition, 'older' EU4 compliant petrol-engined cars are scompliant with the London (and likely all other) ULEZs (EU6 for diesels), and thus you could easily go for a well-kept example of a petrol-engined car from the 2010-2016 period that would be both economical, reliable and cheap to insure / run.

A Civic 1.8 petrol of the 2012-17 model (probably nearer to 2012 for your budget in the expensive second hand price era we're currently in) would be one to seriously consider.

Many others too, including various VAG offerings with the highly regarded belt-driven (not chain driven) 1.4TSI (122PS, 140PS and 150PS versions) and later 1.0TSI (95PS and 110PS versions [newer design so may only be affordable in smaller / lower specced cars and/or earliest examples) petrol engines, the 2L (no turbo) Skyactiv-G petrol in the Mazda3 / CX-3 (2013-2019 car, likely earlier examples only for the budget, SE-L spec good).

Perhaps the somewhat bland but otherwise worthy Toyota Auris ((2013-19) in 1.2T petrol manual form (earliest examples only) might do if you can find one that fits your budget.

I would strongly agree that mileage alone doens't mean a car has been abused, is worn out or not - it is the condition and its maintenance / MOT history and attitude of its owner(s) that determines that.

Never go overboard on the trim specification, as it unnecessarily bumps up the purchase price, insurance and running costs and often the more gizmos a car has, the more likely it is to go wrong as it ages.

Cars with big alloy wheels and low profile tyres (45 and lower) may look nice but can end up costing a pretty penny through extra wear, damage from scuffing, potholes, etc and are often between 33% -100% more than 'ordinary' and 'higher' profile tyres and alloys to replace. the ride on (say) 60 and 65 profile tyres is also vastly better than on 40-45 profile ones, all other things being equal.

The suspension parts also last longer as the extra air in the tyres does more of the work for free. Most modern cars are not 'bad' at handling and should be easily able to take 60-65 profile tyres (normally shod on 15-16in rims) without much penalty in handling. They often come shod on lower and mid-spec trim models, though some upper ones can take them is they don't come with uprated (bigger) brakes.

Often people get rid of older, upper trim cars because the suspension is very worn and the ride hard, and don't want to fork out £££ for expensive parts to get it back to 'just a firmish ride' as it was when new.

Make sure you get in a thorough test drive of about an hour across a wide variety of road types and speeds to get a good idea of how it drives, ride quality / driving position comfort, any issues, etc.

Be wary of cars that have been pre-warmed up (taken out for a decent spin beforehand) from smaller second hand dealers and private owners, as this could (not always) indicate issues.