Yes, there are about 13k genomes deposited in the databses right now, but they are from all over the world -- not just the UK.
But yes, given infinite capacity it would be excellent to sequence from every single patient. It would be a dream, but sadly we're barely able to get enough cotton swabs and RNA isolation kits right now to run a basic qPCR for 10% of the population, let alone get all those viral genome sequences. It would be fascinating to have that many, of course.
You do realise that there are over a million positive samples sitting in freezers in the USA alone. You do know that a single modern DNA sequencing instruments can sequence more than 500,000 viral genomes in one 48 hour run?
But yes, given infinite capacity it would be excellent to sequence from every single patient. It would be a dream, but sadly we're barely able to get enough cotton swabs and RNA isolation kits right now to run a basic qPCR for 10% of the population, let alone get all those viral genome sequences. It would be fascinating to have that many, of course.