This is a grey area and there is no clear published Home Office guidance on the matter. As a non-visa national, you should be allowed to board the return flight without BRP.
When Home Office was approached for a comment, they have stated that BRP-less passenger may be allowed entry after various mandatory checks being performed by Border Force Officer (BFO), including the verification of immigration status using government database. Once they are satisfied about the passenger's identity, they can grant entry with an open-date stamp, writing BRP's unique number by hand above the stamp. In real-life experience, passengers without BRP have encountered great difficulties, with some BFOs reluctant to grant them admission in the absence of BRP. So the usual recommendation is to obtain your BRP at all possible before you reach the UK Border, by getting your returned BRP couriered to you while abroad if you can arrange through a friend or relative. If you have no choice but to attempt to return without your BRP, you are clearly taking a risk. You should not be endorsed to enter as a visitor, as you are not and can create difficulties later when you next try to leave and re-enter UK, as you are only meant to have one valid leave at any one time.
