We decided to get both mobile phone contracts and home broadband with EE. This was a bad mistake in so many ways I can't fit them in this post.
First, the EE sales team in our local shop was slow and incompetent. They lied to us twice saying that that they could cancel our contract with our current broadband provider and start the new one with no overlap (similarly to what you do with energy providers, as you don't pay your electricity bill twice). They also told us that, in case of an overlap, they would have reimbursed us of any money we would have paid the other provider. Guess what? After two months of trying to get two months of overlap back, we have got nothing. Zero.
On top of this, we've had delays in the set up of the broadband, mistakes in billing, and no access to our online accounts for days (they had misspelt both our names and our Gmail account - they had written GMIAL...). And the accounts of our broadband and mobile phones are all separate, which is inconvenient and makes no sense.
Don't make our same mistake!