You should look for competence, how many years in the business, amount of experience they have gained, and if they are approved. They should have the correct insurances in place for example public liability and employers liability.
Larger companies will have ISO 90001, ISO14001. They will be member of safety councils, or safety companies to make sure that they carry all the work in a safe manner together with health and safety polices, and so it goes on. However these companies will be more expensive as it cost thousands of pounds each year to maintain.
If you are unsure that a company is capable of carrying out this type of work to your property speak to their registered body such as the NICEIC/ ECA/ NAPIT ECT.