If my buyers have to get insurance on exchange, does this mean I can cancel the buildings insurance on my current property?
No, we would strongly advise against this. When exchange of contracts happens, you're in a legally binding contract to purchase/sell the house. If your buyer pulls out, you can therefore sue them. However, that would involve solicitors. Now imagine your house burned down in the period between exchange and completion – you could be left with nowhere to live, which does pose a risk if you've already cancelled your policy. If nothing else, you'll have a legal battle on your hands.
It might make things more complicated for you too if you have a joint buildings and contents policy, because you'd still need to insure your contents at the current address. This may mean you'd have to buy another policy for your contents in the interim period, then change it to the new address upon completion. This could then incur a mid-term adjustment fee depending on the provider. It would also mean that you'll then have a separate buildings policy for the property you're purchasing.
The safest thing to do is to keep the existing buildings and contents policy in force on your current property until completion, but to buy a separate buildings policy (and contents too, if you want to avoid any future mid-term adjustment fees for adding this cover) if you're buying a new property too.
A handy tip is to get a quote for buildings insurance and a quote for combined building and contents insurance in advance of exchange. That way, you'll be able to see that any contents element of the policy won't be unduly expensive from that provider when it's time to complete.