The UK has an upcoming COVID vaccine (the Astra-Zeneca/Oxford one) that may prove useful in the near future. Cut off the UK from the rest of the world and the rest of the world can't benefit from it.
Also, it's almost certain that the UK strain is in the US already, and the US is shit at dealing with pandemics once they're on our soil. Border closures only work if your test/trace/isolate institutions and compliance with social distancing is good enough to eradicate the virus from within your borders; they prevent reinfection in that case. The US has shown we're completely incapable of that, so it really doesn't matter.
