As one of your constituents, with some Irish friends from both sides of the border, I was interested but slightly perplexed by your remarks in an interview today that suggest that the common travel area arrangements between the United Kingdom and the Republic of Ireland could be expected to continue largely unchanged in the event of a Leave victory in the referendum later this year.
So far as I can see, this would only be the case if one of three situations applied:
1) That the withdrawal negotiations between the UK and the EU after a Leave vote resulted in an agreement (whether with UK membership of the EEA or otherwise) by which the UK agreed that the freedom of movement rules to which the UK is currently committed by its membership of the EU would continue to apply even after the UK left the EU. I quite appreciate that one can believe that the UK should leave the EU but still accept at least some EU rules, including the freedom of movement obligations - but I get the firm impression that a large number of those intending to vote Leave in June regard the ending of the freedom of movement rules, so far as the UK is concerned, as one of their main reasons for voting Leave, and would regard continuing acceptance of freedom of movement after a Leave victory as a betrayal of the result.
2) That the EU and the Republic of Ireland agree that, while Ireland would remain a member of the EU, the partial exemptions that the Republic of Ireland already has from the Schengen agreement should be extended to a general exemption from all parts of the freedom of movement rules between Ireland and the rest of the EU that would conflict with the combination of the common travel area arrangements and such rules as we in the UK would lay down for the control of cross-border movements between the UK and the rest of the EU. Given the EU's reaction to previous proposals, not only by individual EU member countries but also for instance by Switzerland, to limit freedom of movement, it seems very doubtful that the EU would be willing to accept that a member state should effectively restrict freedom of movement between itself and the EU in order to facilitate freedom of movement between the member state and a country completely outside the EU.
3) That, after the referendum, the government of the Republic of Ireland agrees that a decision of the UK electorate to leave the EU effectively also binds them to do the same, if that needs to be done to preserve the common travel area. In practice, any such assumption looks very much like an encroachment on the sovereignty of the Republic of Ireland.
So, the first of these alternatives seems unlikely to satisfy many of the people who will vote Leave in June; and the other two seem to require the Republic of Ireland either to abridge (with EU agreement, which seems unlikely) or to abandon its membership of the EU in order to preserve the common travel area. I would be interested to know which of these you expect to apply.