I thnk being up in the Wirral the wrong side of the Mersey tunnel will preset problems finding a good installer.
As you now the UK is very SE centric and getting worse. You can't move down there.
I have done a search, and as I expected, the vast majority are based in the SE, and some say they only service the M25 beltway and inside.
It is quite a journey up to your parts from London. Whether you go up the M40 and swing round Birmingham (Awful) or go west on the M4 to the M5, marginally better, it is a problem. Your work will not be done in a day, and so if a crew came form far away, then they would have to stay in a hotel for a number of days. This would be hard to find somene willing to do that.
I did find one outfit that has a site in Cheshire, which is getting a reasonable distance.
For US readers, moving about the UK is nothing like moving about the US. It is major hassle with Kent the worst, with huge accidents on almost a daily basis blocking either M2, M20 A2 and M25 for hours. Kent has the highest serious accident rate in the UK. Just follow
KentOnline for a few days.
Anyhow I have done some research. Richer sound offer HT. They will come to your home and advise but do no work. Of course they are UK wide. I would not recommend that route.
This outfit is CEDIA certifified and at least slightly NW of London in Berkshire, so close to the M40. You would have to aks them if they would go to Liverpool. I would not go with small outfit, that is not certfed unless I knew the guy well and or knew good frinds that had used him and be able to look at his installs.
This outfit is in Royal Tunbridge Wells Kent. Lots of money about there. There are the wrong side of London and not CEDIA Certified. Doubt they will be any use.
This outfit is the right side of London, off the North Circular road which is a pig. They are not CEDIA certified.
This outfit is in Sevenoaks Kent, so right off the M20 but the wrong side of London. They are not CEDIA Certified.
This outfit is more promising for you as they have locations in London, Leeds, Cheshire and York. They are not CEDIA certified, but I would check them out given that they have a presence in Cheshire.
Kent Home Cinema, I'm slightly familair with. They are CEDIA Certified and high end. I have no idea if they would go to Liverpool, but I would guess unlikley. If they would go to Liverpool they are likely your best bet.
This outfit is in Middlesex and so the right side of London, and CEDIA Certified.
I have just found this one, not CEDIA certified but in Manchester which is close to you.
I would call the CEDIA certified outfits first and then the one with the Cheshire location and the one with the Manchester location.
Good luck. Getting this done at your location may not be easy, even though you are in a major metropolitan location. I assume you have looked at your local Liverpool environs.
For what you want you do need a well healed and experienced outfit. Make sure they give you references to contact. You can waste a lot of money doing what you want to do, so be very careful.