Usually the purchase of a business (and one which actually trades from physical premises) has two aspects to it;
1) The sale/purchase of the goodwill and assets;
2) The sale/purchase, transfer, or taking of a new lease of the trading premises.
The process largely depends upon whether the business premises are owned or rented by the current owner. It is also worth bearing in mind that VAT is not usually relevant where the buyer and the seller are VAT registered and where the transaction qualifies for ‘TOGC’ status (Transfer of a Going Concern).