of the brands you mention, Worcester and Vaillant do well in "Which" surveys, as does Viessmann (which was marked down for parts not being widely held). Since mine has needed none in 16 years, that does not concern me. I would be more concerned by a brand that was so unreliable its parts were sold in every high street.
Have a look at the manufacturers websites and see if they have an "approved installer" scheme. You will often get an extended warranty if you use one.
Occasionally there are "special offers" when business is slack, but this will not apply in the middle of a cold winter.
A local independent near your home, who's been in business for years, can be a convenient choice. Check that you are not using a flybynight company. Companieshouse will tell you. Look on the Gas Safe register to see who the qualified people are, so you will be able to tell if they're the ones who do the work. Local independents sometimes have a father and son team.
See if any of your neighbours or local friends have recently had an installation and annual servicing.
You mention you have no hot water, so I deduce that you have no HW cylinder. This is an unfortunate result of combis.
As your system is fairly old, it will probably need a powerflush and a magnetic system filter included in the quote, and most likely, new TRVs. You may as well have the lockshields done at the same time, and any radiators that are too small to keep the room warm, or show any signs of rust.
This will not lead you to the cheapest bid.