Members can travel on parliamentary duties more or less where they wish. Most members' travel, which is reimbursed, is through IPSA, the Independent Parliamentary Standards Authority. Therefore, it's not my responsibility, and so I have to be cautious.
Most members' travel is between the constituency and Westminster. That doesn't include select committee travel, which is paid for by the select committee budget, but if members wish to be reimbursed for travel elsewhere, it is up to them to show that it is for a parliamentary purpose, as opposed to, let us say, a party purpose. If there is some parliamentary purpose—let us say one of their constituents is in prison in another constituency—then they can, as I understand it, reclaim the costs of travelling to that place.
The vast bulk of members' travel is on the fairly simple line back and forth between the constituency and Westminster, and then travel within the constituency, which is also reimbursable.