no it would not
Cloud has 2 elements.
IaaS = somebody elses computer, on which you design and build your stuff
PaaS = somebody elses platform, on which you build
So with the former, you have a TON of extra work to do, to make, eg the database scale, to ensure it does backup and recovery, failover, monitoring, etc - and you have to test all that. and you have to take the never ending set of security and feature patches that also need testing and deploying. This costs a lot of money
But with the later, the cloud provider is doing all that, and spreading the cost over millions of customers - so you get a LOT of stuff for free
Sure UK Gov could try to compete with AWS on AWS's home turf, but do you really think they could? Would they have the money to hire the same caliber of people? Is there any chance at all they could keep up? No. None whatsoever.
Which leaves the gov doing one of these:
1. building only on IaaS which is absurdly slow and expensive
2. using the PaaS then being kicked for this mythical lockin thing as though the costs of moving werent 10x the savings. or the costs of being able to move werent 100x the savings
PS there was a UK cloud - it was actually called UK cloud - they went bankrupt failing to compete with AWS