It is unlikely, but not impossible. Most legal aid these days is means tested. This means that most of the time you will not be given legal aid unless you can prove that you cannot afford to pay your court costs. There are some areas of civil law (as in non-criminal, which is the heading small claims fall under) that legal aid is available for, including compensation for personal injury.
You can use the tool on the gov.uk website to check whether you may be eligible, but you may want to speak with a legal adviser who can give advice on whether you will be entitled to legal aid for your specific claim.