No - i don't believe that is the case. As I understand it, your existing MOT takes precedent over a fail. It doesn't make much difference anyway - if you drive an unroadworthy car then you risk having the book thrown at you, even if you have a valid mot certificate.

Yep, that's how I understand it, too.

You have a MOT certificate. It's clenched firmly in your right hand, and doesn't expire for another three weeks. It's valid.
You have had a fail, yep - but, at the time you're stopped, you may have already fixed the faults. Or they're ones that don't render the car unroadworthy anyway.

So you're legal.

Or you have faults that render the car unroadworthy - in which case, it's illegal whether or not Mr MOT has pointed them out to you.

That could very well be the case - I dunno.

My suspicion is that if you went for an 'early' MOT and your car failed, and the next day you went to the PO to renew your road tax, I think you'd be in for a shock - it's all instant central-computer records these days. And I think it'd be "the computer says 'no'..."