The previous tenant's names probably are on the Lease but on your purchase your solicitors should, in most cases, have sent notice to the freeholders (if specified in the Lease) of the change of ownership/charge.
Maybe best to check whether or not they did as there could have been an address change or slip up but they should serve it properly if required. It's often a lender requirement as well.
Sometimes the lender takes on the responsibility, the solicitor is to send them the notice and then they send it on so best to check.
Your mortgage would have gone through regardless as the property was legally transferred to your name and the bank's security registered.
Check with the solicitors who did your conveyancing and if you don't get any help from them as regards the outstanding ground rent etc... try the local Citizen's Advice Bureau.
Make sure that the freeholders do have insurance in place.
As regards the arrears from the previous owner, this should have been sorted before you completed on your purchase. Your solicitor should have checked whether there were any ground rent arrears and obtained some kind of agreement for payment so check with them whether anything was done.
Make sure you keep copies of all letters you send and send them by recorded delivery.