As you say, too fast for a fixed penalty.
Nothing you have said suggests you have a defence. If you plead guilty you will be fined a week’s net income, a “Victim Surcharge” of 40% of the fine and prosecution costs of around £90. Although a short ban is possible, the overwhelming likelihood is six penalty points.
There’s little or nothing a solicitor can do for you which will significantly alter that and to engage one to represent you will probably see little change from £1,000.