Cannot add much to what FP has said, free consultation definitely worthwhile as is Pepipoo.. There are also plenty of solicitors who have a page or two of generic advice in their websites. If you read up a few of these you might pick up some general trends.

A word in defence of CAB with declaration of interest that I am both an employee of and volunteer adviser in my local town. This stuff is a specialist area and way beyond scope of generalist advice from folks who are not lawyers.

Although we have a national identity an logo we're actually a federation of local charities. What can be offered depends on local funding and, for legal specialisms like this, willingness of a local solicitors firm to provide a pro-bono service. We had a motoring solicitor for a while but there wasn't the deamnd to make it viable long term.

Assuming you intend pleading guilty, save your time (and perhaps money) and don’t bother with a solicitor. There is little one can do to alter the outcome.

Sentencing for speeding is fairly prescriptive. 51 in a 30 limit is 1mph too fast for a fixed penalty. The matter will be dealt with in court and almost certainly be heard under the “Single Justice” procedure (unless you request a court hearing). The guideline penalty (for a guilty plea) is a week’s net income and 6 points or a short ban. Six points is the most likely outcome though if a ban is considered by the Single Justice a normal court hearing will be arranged and you will be asked to attend. You will also pay £85 prosecution costs and a surcharge of 10% of the fine (Min £30, Max £170).