Although I do see what it is you are trying to achieve here, I do feel it best to temper expectations and prepare for a bit of a disappointment.
Firstly, yes as @Andrew-G advises, be very wary of cancelling your existing Sky contract, lest you find yourself without anything for a while - in fact if you intent to keep the same telephone number and port it to VM, then you absolutely MUST NOT give notice to Sky. Any pending cancellation or cease orders against the line will 100% stop the port from happening - this is a OFCOM procedure nothing to do with VM or Sky.
Secondly, do you happen to live in a bungalow? Odd question but the VM installers will not do any work above first floor level - and sometimes even then they can take some persuading! Anything higher requires a special 'working at heights' trained installer. It is more than likely that they will refuse point-blank to run the coax up to the loft.
The pre-install team come first and run the coax cable from the street cabinet or the 'tee' outside your house to a box which they will attach to the outside front wall, this cable should be protected by trunking and properly buried under the garden, although there have been some quite spectacular variations on this reported on here. Normally when the installer comes, they drill a hole through the outside wall, run coax in and then to wherever you want it - drilling through internal walls or running the cable along the skirting boards as appropriate. In your case, you would be asking for a cable to be run from this 'omnibox' up the outside of the house and into the loft, and this is where I fear, you will get a 'sorry but no can do' response!
But let's imagine that we get past that and a coax cable gets up into the loft a connected to a Hub4 - connect your switch to one of the ports on it and hence you will have ethernet connectivity to the various rooms - so far so good. What provision have you made for WiFi throughout the house? The WiFi provision on the VM hubs is, well, less than stellar, I would say that the chances of you getting any reasonable WiFi other than in the room directly below where the hub is, is probably slim to none. Do you already have WiFi access points connected via ethernet throughout the house? VM will offer you their 'pods' which are WiFi extenders and you will be entitled to three of these for no extra cost on the 1 Gbit tier. These may well work OK for you, failing that you will need to make your own alternative arrangements.
Now moving on the TV provision, yes each of the boxes needs a separate coax feed as well as a network connection (which can be ethernet (best) or WiFi (often sub-par at best)). The coax would-be split into four at a convenient point, presumably up in the loft, and there may be a need for a powered splitter to be fitted if the signal strength is a bit low. One of these goes into the hub as mentioned above and the others need to be run to which ever rooms you want the TVs in. Now you say there is already coax between the loft and the rooms - but is it suitable for cable TV distribution? Satellite-grade coax, might look like cable coax, but doesn't necessarily have the right electrical characteristics, neither might the sockets in the various rooms.
Now on this point I can see four possible outcomes;
a) The installer just takes a chance and uses the cables, on the grounds that he gets away early. If it isn't suitable, then he'll be long gone before you notice the miserable experience you'll have.
b) The installer makes measurements, tests the cable and decides that it is all OK and uses it - all good. This is actually very unlikely to happen.
c) The installer tests the cable, realises that the signals will be a bit borderline, but uses them anyway, he gets away early, it all appears to work at first while he's there and when it all falls apart later then that's your problem guv!
d) And this is by far the most likely, the installer takes one look at the existing coax, refuses to even touch it and starts to drill holes through the ceilings and walls to run the 'proper' coax!
And lastly the phone, these now have to connect directly to the hub, this is not negotiable. I expect the installer would connect a phone to the hub check it is working and then clear off. You'll either have to go up into the loft to make a phone call or do exactly as you suggested and run your own twisted pair cable between the hub and wherever your existing socket is and connect it up.
Now despite appearances, I'm really not trying to put you off signing up with VM, just pointing out that this is likely to be very, very far from plain sailing.
