How to register the purchase of a lease

We purchased the lease from the leaseholder in 2010.  In making a change via our solicitors for tenants in common we note the lease is still recorded.  What do we have to do to register our purchase?  I have the 'Chief Rent Purchase Certificate' from the lessor.

Barry - if you purchased a registered lease then the tenant/owner would need to transfer the ownership/title to you - Registering land or property with HM Land Registry: Change the registered owner name - GOV.UK

Thanks Adam, but I'm a little confused.  We are the property owners already and are mortgage free.  This came up when we did our wills recently and protected our son's inheritance by putting the property into a trust.  The resultant letter from HMLR identified the land rent as still being in force, which it isn't.  It is this that I want to correct, not the title to the property, we already have that.

Barry - your confusion is shared as I'm unclear as to what letter we would be issuing that refers to 'land rent' 
What's the title number on our letter please and what was it's date?

Hi Adam,  You didn't issue the letter - the Lessor did.  We paid them £300 in 2010 to buy the lease from them.  We have their confirmation letter of discharge.  I just need to know how to present this evidence that we are now Freehold to the Land Registry so it can be removed from our Title.  Hopefully that explains it better.

Hi Barry - unfortunately it doesn't explain things any better. The Lessor will be the freeholder/landlord/superior title holder.
If you bought the freehold to your lease then they would have had to transfer the freehold title to you. And I assume by remove you mean you then want to merge (close) your lease and simply own the freehold.
If they have sold/transferred the freehold title to you then our online guidance explains how to apply to register that - Registering land or property with HM Land Registry: Change the registered owner name - GOV.UK 
What also doesn't make sense includes why that didn't happen in 2010

Hi Adam, thanks for the explanation.  I think I'll write back to the 'Ground Rent Specialists Company' and ask why they haven't transferred the freehold title to us.  Their letter simply says keep the certificate with our deeds but now everything is electronic we need to ensure the freehold is reflected on the title to the property.  Many thanks for your help.