The Section 21 is to terminate an AST at the end of the fixed term. You must give two months notice. You can issue a Section 21 at any time during the fixed term. You will only have problems if your tenant fails to leave once the Section 21 expires. If she has emailed you confirming her intentions and you have agreed, then it's probably a good thing that you have it in writing (emails are admissible as evidence in court). Sounds like you won't have any problems in that regard.
What you might have a problem with, is if she leaves and there are issues with cleanliness, damage, unpaid bills or disconnected services. If you consume the deposit as rent (and if the deposit is properly protected in a custodial or insurance based scheme, as it should be by law) then you're not really supposed to use the deposit against rent - and what she says now may be all fine, but if she disputes the use of the deposit later, you're up sh*t creek without a paddle.
It really depends on whether you want to trust the tenant to make good on her promises, or is she under so much financial pressure that she's looking for any way out?
The best thing to do is stick to the standard rules - you can release her from the contract early, which would mean you haven't used the deposit and if there are damages you can still keep it to pay for them.
If you're looking to re-let and don't want to pay huge fees, try going solo. There's loads of resources out there to help you so you can avoid agents fees. Failing that, try a company such as Visum Ltd.
if you need any further legal help I'd suggest speaking to a local conveyancing/property solicitor.
Hope it works out
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