It is reasonably common to be invited out for lunch by a business contact in the UK, but more unusual to be asked to go for dinner.
Business lunches are often seen as an extension of the meeting and it is usually acceptable to discuss business matters over the food. If in doubt over this matter, follow the lead of your host. The person who invites will invariably pay and there is no real need to offer to contribute to the cost. If you have invited a guest and they offer to contribute, they are probably doing so out of politeness and do not necessarily expect to be taken up on their offer.
Lunches can vary in style from a very informal pub meal to a much more elaborate formal meal at an expensive restaurant. The choice of venue can depend on a number of factors such as location, importance placed on the business opportunity (or guest), market sectors etc. If you are unsure where to take somebody it is best to err on the side of caution and go to a good quality restaurant.
Alcohol will usually be offered at lunch and some British business people will accept whilst others prefer to stick to soft drinks — this is an entirely personal decision and you will not be under pressure to drink alcohol in this situation. It is much more common for larger amounts of alcohol to be drunk at dinner and on these occasions you may find that you are placed under a small amount of pressure to join in the drinking culture.
Most restaurants add a service charge to the bill automatically, but it is still customary to give an additional tip of around 10% directly to the waiter.