OP, what a horribly worrying situation for you.
I'm a landlord, of the accidental variety. I would be delighted, in your landlord's shoes, to agree to let you withdraw your notice, unless I'd found a new tenant already, or you were behind with your rent. The prospect of having a tenant leave in the middle of the Christmas holidays, and possibly an empty property for a while in the depths of winter, is unlikely to fill any landlord with joy.
Letting agents sometimes take a more bureaucratic view and they also benefit by way of extra fees each time the property is re-let, so they may have a different perspective.
The agent will have to take instructions from the landlord so he/she will be contacted anyway, it's not the agent's decision. If you have the landlord's email I would be inclined to email them direct (or failing that, write by first class post) copying the agent in so that you are not going behind their back - and making sure to keep the email/letter strictly business-like in tone.
This is a long shot but it's worth checking your tenancy agreement to see what it says about service of notices. If there are special requirements, such as email not being a permitted method of service, your notice may be invalid anyway.
Also, if your initial fixed term has ended and you have moved onto a monthly periodic tenancy, did you specify the correct date in your notice? You must give at least one clear tenancy period's notice, and the notice end date must be the last day of a tenancy period (ie the day before a rental payment is due). If the wrong date and/or insufficient notice was given, the notice is also invalid. This stuff is actually surprisingly easy to get wrong - it bites landlords on the bum often enough when they are the ones serving the notice.
Of course, Murphy's law dictates that you will have served an irritatingly perfect and watertight notice, which can't be retracted unless the landlord agrees, but it's worth checking.
If your notice is invalid, that strengthens your position - but obviously if you have to rely on a technicality to force your landlord to let you stay, it isn't a great basis for a good ongoing relationship. But might at least buy you a few extra months to sort the situation out.
Good luck.