No. There is no need to visit a solicitor. Once you have completed the deed poll you simply need to get someone to witness you sign the document. This person should be at least 18 years old. They should not be a relative or live in the same house as you. You may choose to get a solicitor to witness your signature but it is not necessary.
We supply our deed polls to solicitors and public notaries. We dare not ask how much some solicitors charge when providing a name change service but it is typically between £80-£100.