I’d say go the pcp route on a nearly new second hand car. You will need a deposit, but if you’re able to get some money from the previous car that is how you should use it. The key things are to get the agreement over as long a term as you’re able to get (can be over 60 months). Cars up to 3 yrs old can be bought this way. Beware the final payment is what’s called a ‘balloon’ payment. So something like 30-50% of the purchased cars sale price. This won’t be a problem when you come to it because you can either text-finance that amount over 3+ yrs and keep the car or start from scratch (it won’t be yours to trade in). Factors like low annual mileage and the cars depreciation will determine how much you pay per month.
As an example I had a Volvo C30 a year after they came out brand new. The car depreciated slower than they’d factored in so I actually had some equity in the car at the end of the term. It would have been a car that I couldn’t have thought was within my budget but signing up to a pcp was the right thing for me to do at that time. I traded in a car worth £2800 at the time and had 48 monthly payments at £140. At the end of the term I took out a loan for the balloon payment and the car was ‘mine’. It was fantastically reliable, had 2 years manufacturer warranty remaining and was economical to run. So good I bought another faster one on pcp some years later.
Your job is steady work, you have good income, so your only stumbling block is to get that car you have traded in (a dealer won’t see it as such a big problem to replace a head gasket, the part to them is cheap, and the hourly rate for the work is an overhead to them, not something to make a profit on to a customer).
My advice is to pick a car that won’t depreciate too fast, also downplay your mileage (no one will check) and stretch the payment term to as many months as you can. If all goes well you’ll end up in a car that won’t let you down and won’t cost you anything beyond fuel, insurance and wear and tear items like tyres and brake pads.