In most cases, clients prefer a set cost for a project over an open-ended one. If a project spans over a few days/weeks a client will prefer a project fee instead of hourly; Instead, they need to know how much it will cost them for the entire Project.
When you are calculating a fee for an entire project the place to start is to make a list of all the elements involved in it; How much research and prep time will you need, how many sketches will you show, so how many rounds of revisions will be needed to get the final result, is there post-production work involved, will you require any travel for meetings with your client? Take everything into account so you avoid underselling yourself and the value of your time.
Once you have calculated how many hours the project will take, multiply that by the hourly rate. This number is your baseline product rate. Now do some research on the industry rate for this type of project; If it is higher than your baseline project rate perhaps you should increase it by £500 or £1,000 to better match that standard.
If that’s some point during a project you realise it’s taking longer than you expected due to the client, be sure to let them know immediately rather than surprising them with an unexpectedly higher bill at the project’s conclusion. Over time you may become so familiar with how long it typically takes to develop something that you can offer an á la carte menu of rates for your most called upon services.