Overpay mortgage or save for lease extension?

CapabilityJones

I have a shared ownership house that I've been living in for about four years and it's leasehold. As of January this year I have 88 years left on the lease. I gather from various articles that the cost of renewing the lease rises dramatically at 80 years so in theory I've got a while before it's an issue, but I don't intend to stay here that long and would hopefully be looking to sell in 1-3 years time, life circumstances allowing, and I'm not sure if an 85 year lease might make it less attractive to potential buyers.
I'm in a position now where after several years saving and budgeting, I have about £400 a month 'spare'. I was previously putting that money into savings but I just hit 10k in my emergency fund (which is about 8 months expenses for me, so more than enough) and I'd like to do something more useful with the extra every month. 
My first thought was to overpay my mortgage, which is what I'd really like to do, but then I wondered if I should put the money aside to potentially pay for a lease extension instead. I had a look and an extension will probably cost around 6k. Obviously I have the emergency fund, but that's for emergencies, which this isn't. I also don't really know how much of an effect the shorter lease would have on a sale - it's not short enough to affect someone getting a mortgage I believe. And it's possible that I could be looking to sell next year with around 87 years left, which isn't that bad.
What would you do? Focus on overpaying the mortgage and see how everything else plays out, or put the money into savings and aim for the extension?

MovingForwards

Another option is to sell and simultaneously extend the lease.

Have you looked up the procedure for extending the lease and potential costs as I believe it's different with SO, compared to 100% ownership. Others will be able to comment.

enthusiasticsaver

Have you spoken to an estate agent as to how much value increasing the lease period would add?  I know if it is less than 80 years it is not mortgageable (or that used to be the case) so you might be better reducing the sale price by a few thousands instead if that is all it will add to the valuation. Moving forwards makes a good point that you will have solicitors costs and presumably land registry fees too which might be cheaper if you did this on sale rather than a separate issue. The shared ownership complicates it too. 

 I would overpay your mortgage with any spare money as £10k is a decent emergency fund although obviously if you intend moving you will need to cover fees etc. How much equity do you have?