Lease extension valuations are done on a fixed formula. There are several calculators on the Internet and the formularies quite complex. Here is one calculator. http://www.myleasehold.co.uk/lease-extension-calculator
The amount the freeholder can charge is based upon a statutory formula. There is no legal reason why you cannot agree whatever price you like between you however. How much you are paying may be over the top or cheap. Or it may be the correct price.
The reason that you have been told to get a valuation is so that the can be no allegation at any stage in the future that you were not advised correctly by the solicitor that you may have been able to buy the freehold cheaper and that the freeholder can never make an allegation against his solicitor that he could have got more money for it. Hence, it is in both your interest.
I can’t see why you have to give notice of the lease extension to the freeholder because the freeholder has notice by virtue of the fact that you are having the lease extension.
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I can see now why the solicitor is insisting that you have a valuation done. He is covering his back to prevent any allegation in the future that he has been negligent in failing to advise you in respect of the cost if you are paying double what the landlord is actually allowed to charge you.
It’s not a case of giving permission for the lease extension, he has to extend it. You have a statutory right.
If the solicitor doesn’t deal with lease extensions, find another one.