In short, no.

Under normal circumstances, you would be able to insure the car and then take it to an MoT station for a pre-booked appointment. However due to the Government lockdown, I do not think this will be advisable. If you were to experience a breakdown for example, you would place unnecessary pressure on your local emergency services who may already be stretched due to the coronavirus outbreak.

I would recommend waiting until the lockdown period has ended, before getting the car insured and then arranging an MoT and road tax.