I need help on a contract law question?

You are indeed in breach of contract. The companies' remedies will be covered by the terms of the contracts, and any company with half a brain will have insisted on signature of a contract they have had drawn up in consultation with lawyers. The normal thing to do is charge a non-refundable deposit in case of cancellation.

The band were sensible enough to do this, so they keep your £1,000 provided it is stated in the contract that it is non-refundable, and that's that. No way are you getting this back as if you sue, the judge will simply point out that this is normal terms of business, these are not unfair terms of business, find against you, and possibly award the band's legal costs against you as well. The deposit is compensation for them in case they can't find another gig the same night at short notice.

The catering company MAY be able to sue you for costs incurred so far, though if you cancel a reasonable time in advance these are likely to be small and not worth going to court over. Cancel the day before the party and they will already have bought all the food and have wages to pay for preparing it, so they are far more likely to sue to get that paid for.

On which point, timing is important. When my family used to go abroad regularly on package holidays, it was always in the small print at the back of the brochure (we're talking 1970s here, no Internet and it would be booked from a brochure we picked up at a travel agent - you booked by post or took the booking form back to the travel agent) that how much of the price of the holiday you forfeit depends on how far in advance you cancel. As I recall, it was 10% deposit with the booking form, which you definitely don't ever get back, the final invoice for the rest is payable 8 weeks before departure, and cancellation charges are on a rising scale ending with if you cancel less than 2 weeks before departure, you get nothing back because the company is unlikely to be able to resell the holiday at that short notice. We actually had to do this once because Mum had to go into hospital shortly before we were due to go to Italy, and Dad had to claim the cost of the holiday back from the travel insurance company. Having to go into hospital was an acceptable reason to cancel for the insurers, so he got the whole lot back from them. (What we actually did then was that Mum and Dad pooled that payout with the holiday budget for the next year and we all had a winter holiday in Florida instead. I don't suppose I would ever have got to Walt Disney World and Kennedy Space Center if Mum hadn't been ill!)

Talking of insurance, there is such a thing as wedding insurance to guard against cancellation of the wedding.

Yes you are in breach of the contract.

Since the band was still willing and able to perform at the time of canceling for the agreed upon date they get to keep the deposit, but are not due the remaining $4,000.00 as long as you give them reasonable amount of time to find another gig. If you cancel day/week before, they might not be able to reasonably find a replacement venue in time and so are due the remaining $4,000.00 for being unable to find a replacement gig. EDIT: (Assuming they can show that $5,000.00 would be a normal amount they would earn for such an average day.)

The catering company is allowed to bill you for the costs they had already incurred, the food purchased, the staff hours worked on ordering said food, equipment rented specifically for this event, etc. Otherwise they are not due anything.

Yes you are in breach and depending on your contract terms with them about cancellation you may have to pay them both the full amount.

You have at least lost your £1,000 deposit and if the catering company didn't take a deposit ( which they would so it suggests this question is about homework help) then you need to come to an agreement with them about any cost they have incurred or they could take to to court