I'd want a UK company to do it for security reasons and for the econmic benefit of the UK economy at much as possible.

That should be the default position and thus require an argument (a much better one) why a British company/the UK gov should /not/ deliver it.

Would you have a problem with a Russian company delivering the project...?

What if an American company delivered it? American companies already control the platforms the apps will run on (so they you cannot secure it against them). On top of that the server side will probably run on an American owned platform too.

As fir the economic benefit that implies rejecting the idea that free trade is better, which is a fundamental assumption made by western governments.

I actually would like to see it happen, but one aspect is pointless without wider tech sovereignty, and the other would require a revolution to be accepted as a reasonable argument.