You need to be careful about data limits. Fibre packages often have various data caps. I use at least 100MB a month, often more and I am a single person not at home that much, so a family who are using lots of devices I expect would use quite a bit more data.
Looking at the Virgin media £4 deal... you MUST read the small print:
SERVICES AVAILABLE IN VIRGIN MEDIA CABLED STREETS ONLY.
Installation charges apply. Must pay by Direct Debit and use eBilling or the cost is higher.
The £4 is for first 6 months, then it goes up. You must have Virgin Phone (so presume that means line rental) which is £15.99 a month.
It is not unusual for there to be terms and conditions.
PlusNet has various terms and conditions. Looking at their 38Mb package, the terms include:
£15.95 a month line rental. 18 month contract. Reduced price for first 9 months.
If considering having Fibre Broadband using your BT (now Openreach) phone line, then read FAQs on the Broadband providers site. Some will offer Line Saver. PlusNet: Line Rental Saver costs £155.88 for 12 months line rental (monthly equivalent £12.99). So you can get a saving, though quite small, by paying line rental a year in advance.
Sky TV - That comes via a Dish, so yes you can have other providers provide Phone, Internet, or both. You should look at what difference that makes to your Sky price, as if you currently have everything with Sky, then you may have a package deal and won't qualify for that if you downgrade.
Sites like Quidco offer CashBack for taking out subscriptions of this type, it can be quite high at times. Over £100 back for taking out Plusnet Fibre today. If you prefer charity donating, then sites like EasyFundraising also have offers for Fibre Broadband subscriptions, so your nominated charity gets a donation (though it can be a lot less than Quidco for some reason).
As you want to keep Sky I would initially ask Sky what deal they will do for you to upgrade your package. Look at the price over the full length of the contract. Then compare to other providers, again calculating the total cost over the length of the contract. I would also suggest going for Unlimited Data packages, as once you have faster internet, you will stream more movies/TV.