Your solicitor will ask you for a certain sum of money to cover the searches which they need to carry out on your behalf. They cannot submit these until you have paid the sum requested. Local Searches often take up to 4 weeks(or more!) and if you are keen to move the process forward then the sooner this sum is paid the sooner your conveyancer can apply for the searches as until the results are received they cannot proceed to exchange even if all other enquiries have been satisfied. Most conveyancers would be unwilling to exchange "subject to searches".