Where you stand legally is that you have a right to not have to deal with the flood from your neighbour's property. The tort of nuisance is a common law term which means your enjoyment of your property is being affected by your neighbour due to their inaction.
You should speak to the council to see if they can intervene here - if they can then fine, no legal action is required. Legal action is a last resort and the courts expect parties to explore other avenues if at all possible.
If nothing can be agreed then you will need to apply to the local county court for a civil injunction.
However, before you do this, send the neighbour a cease and desist letter to warn them of your intentions unless they confirm they will stop the flooring, at their expense (and give them 7 days to stop their conduct). A template “cease and desist” letter is available at https://www.lawdepot.co.uk/
If you go to the search box in the top right corner of the site, it will bring up a list - you want the "general" letter.
You can use your own letter if you wish - it just has to make it clear this is a cease and desist letter, that you demand they stop their conduct, and that if they do not within 7 days you will apply to the court for the injunction and seek your costs.
That letter may well be enough to stop the conduct - as an injunction is a serious legal remedy.
Assuming they continue, you will need to complete the application for the injunction and send to your county court with a fee of £308 payable to HMCTS (unless you have a low income/low savings and/or you are in receipt of benefits in which case you can get a fee exemption so you do not have to pay).
For a fee exemption you need to check your eligibility here:
http://www.gov.uk/get-help-with-court-fees. If you do not qualify for the fee exemption, you can pay either by cheque or attend the court and pay at the counter. You will need to prepare a witness statement to accompany the form.
You will need to detail the history of the issues with the neighbour to paint a picture for the Judge as they will not know what this neighbour is like and what they have done to you unless you describe it. Your photos and the videos can be shown to the judge to support your application for the injunction.
If the injunction application is successful you can ask the court for a costs order to be paid by the neighbour.
The court will list a hearing where you attend and ask the District Judge for an order and the injunction. The application would be made under the tort of nuisance as I mentioned above.
If granted, the Order is then served on the individual concerned and they are bound by the court order - if they breach the order, they are in contempt of court and could well face a fine and a prison term.
The cease and desist letter may work so you may not need to apply but if you then I recommend you go to the court in person with the forms to ensure they are correct - they are fairly complex so it would save time by you doing this - the court staff should check them before they issue the papers.
If you do need to take that step and apply for the injunction, please come back here as I have the forms required. If you prefer a law firm to do the letter (and apply for the injunction if the letter has no effect) then try any of these firms they should be able to claim their costs from the neighbour so would be worth asking them to help you with this: