Yes of me! you just stalk me around. It's rather flattering.
Imagine if they had to consult their constituents every time they voted in parliament.
Well they don't, it would be impractical. They don't this time either: it's already been done.
If there is any moral duty it is to vote for what an MP truly believes to be the best interests of his/her constituents and the country
So we are basically back to what I said earlier: the legitimacy according to you lies in the MP's own moral compass.
But that's not true at all: it lies in the fact that they have been entrusted by majority vote to use their moral compass appropriately. This is where their legitimacy lies. When there has been a majority vote by every one of their constituents and the result of that majority vote is a Vote Leave, it is their moral duty to observe the legitimacy of the majority vote - which is after all from where they draw their own legitimacy and authority - and vote with the majority.