Flying Domestic within the UK getting into T5 at 0720 and then out of LHR on QR at 1050. This should be enough time to collect and recheck luggage?

I will be travelling on two tickets as the original ticket I had just bought from LHR only so will BA be able to check us through from our Domestic UK segment?

We will be flying Business on QR but since we are on separate tickets BA will not honor the luggage allowance right?