I’ve extended a lease with Westminster Council on an ex-council property so have some experience. Westminster would only countenance an extension of the lease under the statutory provisions applying to long leases, not as a matter of free negotiation. So first I had to have owned the leasehold for two years (so I had to wait), and then they would only do a 90 years extension (not for instance a 10 or 30 year extension). It may be that Camden takes the same view.
As for what the lease extension will cost, the pivotal question is whether the lease has 80 years or more left to run. If so, the lease extension should not be more than a few hundreds or thousands of pounds + legal costs of another thousand or so. If however the lease is significantly less than 80 years then under the statutory regulations, the leaseholder has to pay half the marriage amount (which is the increase in value of the property when the new 90 lease is married to the existing lease), which may means tens of thousands. Anyway, it’s a statutory calculation and there are several easily googled websites which will indicate what the cost will come out at for your particular parameters.