see this bit here
'You are to vacate the property no later than 12 noon on Monday 25 July. Where upon we will carry out our full inspection the following week, returning your deposit as appropriate.
We will not be communicating any further on this matter. We are, as you know, away for most of the month of June. When we return, we will be putting in place a Letting Agent, who will require to be into the property and gardens to show prospective tenants the property for rental, all as 4.3.10.3 of the Agreement.'
Well they can't do that. You do not have to vacate until two calendar months after you receive the notice to quit in writing. Do you know (Hissy?) whether this has to be a section 21 notice or just a letter stating notice?
So they are getting back at the end of June, and don't intend to communicate further with you. Well then you just stay put
and when they get in touch when they return point out that they haven't served the correct notice and when they do, you will vacate two months after that date 
They should also make arrangements to inspect the property on the day you vacate, or the day after. They have to return your deposit in a timely manner, there is something in the DPS about that.
Thank fuck they are getting a letting agent. They will, at least, know what they can and can't do WRT visits.
Oh and does anyone know what you should do about rent if their notice period doesn't correspond to a rent date? So if they gave notice and you had to leave on 31st July for eg - do you pay 7 days worth of rent on the 25th? Or not at all? Seems as though they do themselves out of rent, potentially.