A lot of really poor information in this thread.

1. OP departed from the EU. Therefore UA's "duty of care" under EC 261/2004 applied. It includes hotels & food. While I doubt that UA will cover 4 days because it likely would have returned OP to the UK via one service or another, at least the first 1-2 nights will be covered. So long as OP's expenses are documented with receipts and submitted with his claim under the Regulation, he should not have any issue in reimbursement. The balance will be covered by his travel insurance.

2. UA does not stop people from boarding their flights because they may misconnect. There are just as many people who would complain bitterly if that had happened in this same situation (although the catastrophic nature of the Houston situation is not the ordinary case). UA has multiple systems which people may check and had a weather waiver in place well before the actual cancellation took place. Passengers have an obligation to do some checking rather than have carriers direct them.

3. UA's "Trip in Vain" provision would have had OP returned to BHX in short order if he had wanted to. UA would have refunded the ticket as well. All on request.