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To be fair, the Estate Agent is unlikely to have a copy of the Lease, as this will be supplied by the Seller's Solicitor to your Solicitor.
The Agent should be able to tell you how much the ground rent and service charge is and how many years are left on the Lease, but they are not obligated to provide this information to any propspective Buyer- although most respectable Agents would provide this information as it is likely to assist in the Sale of the property!
I appreciate you don't want to incur unneccessary legal costs, but a copy of the Lease will be received by your Solicitor at the onset, when he receives the Contract from the Seller's Solicitor.
I would therefore suggest that you ask your Solicitor to tell you once he has received the copy Lease and ask him not to carry out any other work, other than letting you know the terms of the Lease.
I hope this assists and sets out the legal position.