No hot water - should we replace entire boiler or fix divert?

We are having trouble with our boiler and can't get any hot water (heating still works) - before this happened we had several months where the water only got hot if we put the heating on.

An engineer came out today to look at it and he said that the diverter valve needs replacing. He doesn't do Worcester Bosch but said he thinks we will struggle to find someone to do it as there are access issues and the boiler is really old. The access issues are mainly that you can't flip the bottom of the boiler open properly at there's pipes in the way (you can see photos on my rated people job ad: https://www.ratedpeople.com/account/home/my-jobs/10084343). Since we spoke with him we found documents, from before we bought the place, suggesting the boiler was installed in 2003! This correlates with how old the engineer thought it was but our downstairs neighbours are insisting it's only about ten years old (the boiler came with the house and we only moved in three years ago).

The engineer that came out suggested we might be best off getting a new boiler (with him or someone else) but he also said that we could try finding a Worcester engineer to fix it - he thought they might charge about £400 but didn't know.

If we replace it we will need a condensing boiler and a flue, and because we're an upstairs flat we will need access to the roof of our downstairs' neighbour's kitchen - but they're saying that the engineer that came out was basically trying to con us and it's a simple and cheap fix to replace the diverter valve. They're also insisting the boiler is only about ten years old but our documents suggest it's almost 19!

We didn't get the impression we were being misled but you never know and we are not experts at this sort of stuff! Any advice would be really helpful, thanks :)