We have just replaced our boiler and bathroom, and are also in the north west!
Quotes we had to replace the boiler were between around £1800 and £2300. We ended up going for the most expensive one. The quote will generally change in price depending on which boiler you go for, work Worcester or Vaillant being the best. We went for the biggest Worcester one for residential use and it's been great. That price didn't include replacing any radiators so sounds like you have a good deal but check what type of boiler it is and how long the warranty is.
For bathroom ours ended up costing around £6k in total I think. Of that around £4K was the labour and around £2k for suite, tiles, radiator, taps etc.
I sourced all the stuff myself.
We had a range of quotes and I think in general they came in around £3-4K. Some people just quote for the fit and things like the plasterer/tiler/electrician/plasterer can all be separate. Some can do some of that stuff themselves etc
The guy we used was one of the more expensive quotes, but we had a nightmare trying to find someone to do the job and by the time he came out I was ready to throw in the towel. He came across really well and I'm now so glad we used him as he did such a good job and was a total perfectionist. He is coming back to do our other bathroom in March. I'm glad we spent a bit more on him than a few hundred less for a shoddiest job.
My advice would be make sure you like the guy and feel comfortable making requests, minor changes etc. There will inevitably be decisions you have to make during the process such as positioning of things, edges, and you don't want to feel bullied into making decisions.