I think you will find it difficult to get the equivalent cover of the MRP separate from your mortgage. I think the peace of mind is worth it, but plenty of other older threads debate that. The important point is that without re-mortgaging, if you don't take it up at the outset, you will lose the opportunity.
Giving the industry the benefit of the doubt, they see the taking out of MRP at the outset as someone trying to cover a modest risk. If you were to try to take it out later, it would be interpreted as someone trying to cover a near certain risk, so they don't do it.