Hi there! I'm in Sheffield too and we have done the Eurostar a couple of times but we've had a couple of delays and then last time the train stopped, underground, and we had to wait there for well over an hour. It was boiling hot, there were bored/tired/hungry crying children everywhere and quite frankly, it put me off permanently. We then decided to drive and use the Eurotunnel instead and we've never looked back! Is driving not a possibility for you?
We absolutely love driving to DLP for many reasons. It's cheaper and you are going on your own terms. Even if the train is held up, you're not trapped in a carriage like sardines, you can get out of your car and walk around. (We have never had a hold up on the Eurotunnel though).
When you go in the foot passenger Eurostar, you usually arrive around lunch time so by the time you've sorted your luggage and got your tickets sorted, you've missed an awful lot of park time on your first day. The same goes for your last day, you have to leave the park early to get your train. This is another reason we like to drive.
This is what we're doing on our next trip, just to give you an idea... Leaving Sheffield at 7am, driving down to Folkestone to catch the Eurostar around 12.30. Arrive in Calais about 40 minutes later, drive down to the F1 hotel just outside DLP (cheap hotel, cost us about £40). We should arrive at the hotel at about 4pm (it's only a 3 hour or so drive from Calais). Out for dinner somewhere (loads of places locally), back to hotel, good nights sleep, up early, go to Disney hotel for 7.30am, collect tickets, arrive at park for 8am for the start of Early magic hours. We are leaving the park about 6pm on our last day, to catch the 9.30pm Eurotunnel back, then driving straight back to Sheffield, probably get home about 2am. The Eurotunnel cost me £133 return. Bargain! Obviously, you've got fuel costs but our car does about 60mpg and is diesel so it's very cheap!
The drive from Calais down to Disney is soooo easy. All dual carriageway, very little traffic (it's nothing like the M1!) and like I say, we've never looked back and we wouldn't go any other way. We get full use out of our park time, it's cheap, we really like being together in our own little space (the car!) where we can chat, sing, laugh, eat etc without having to worry about disturbing others. We also don't have to think about carting our luggage from A to B to C or fitting everything into a suitcase. We just chuck the stuff in our car and we're off!
If you wouldn't want to do the drive all in one go, there's plenty of choice of hotels in the Ashford area which is only 15 minutes from the Eurotunnel terminal. We stayed in the Travelodge when ours were little but now they're a bit older and we don't have nappies and bottles to contend with, they're fine to do the journey in one go.
Hope you have a wonderful time!