You should be able to buy out the freehold. I have a leasehold property, with a tiny ground rent that has never been paid, but I know that I can apply to the land registry and buy to get it changed, only real cost would be a solicitor.
Also I was involved in a sale for someone recently and the issue of ground rent came up. Solicitor gave two options, agree to pay around 200 Euros or so (which covers the last 6 years of ground rent, statute of limitations applied) or declare that ground rent had never been requested, that's the option we went for and the purchasers solicitor had no problem with that.
But all titles are different so just ask your solicitor.