You may agree to accept instructions from a vulnerable client, or find out after having accepted instructions that your client is vulnerable. If so, the Equality Act requires you to make reasonable adjustments and you cannot decline the client's instructions on the basis of their vulnerability, where such is a protected characteristic (e.g. disability, age). Instead, you will need to set out how you will ensure you are able to act in their best interests. For example, you may have a client with ADHD and thus you may have to read all your letters to him and take extra time to explain them. If so, you should keep a detailed file note of having done so and you should address upfront the additional cost that will be involved in making the reasonable adjustments. The Equality Act may say charging those with a protected characteristic more is discriminatory. However, for a business that charges by the hour and where more hours are required, this would be hard to follow. This is best addressed at the relevant time.
The Law Society has published two excellent notes which you should read before taking on a vulnerable client. See their guide on meeting the needs of vulnerable clients and their case studies on working with vulnerable clients. See also the SRA's guidance on this.