Your solicitors receive the title documents. They have to arrange payment of the stamp duty land tax to Revenue & Customs. They then apply to the Land Registry to record the change of ownership, and also to record your lenders’ charge on the property. After a few weeks, that will be completed, and you will be shown on the Land Registry’s electronic register as owner of the property.
If you are buying a flat, there are some additional steps. Your solicitors have to register the transfer document with the landlord or management company, so that they know to send rent demands and service charge demands to you rather than to the previous owners. If the sellers had a share in the freehold or management company, that has to be transferred into your name and your solicitors will be arranging that too.