Possibly is, my experience with a few current London based clients in my day job is often recieving pushback and delays on any initial deposits or pre-payment. Holding firm that the clearly defined payment terms are a prerequisite for work commencement has been the most effective approach, even if it involves some uncomfortable emails or meetings. Polite but firm push back on a clients reluctance is very often sucessful even if momentarily uncomfortable.
I'd suggest to try proposing reasonable payment terms as soon as possible, terms that are as favorable to you as they may or possibly are willing to accept, and upon discussion (or a note included in the proposed terms) respond that an initial deposit is a firm requirement before commencement of any billable work, but you are flexible and willing to discuss a customized draw (payment) schedule if it's required (or.. you're not willing). You may be surprised how many clients will accept your terms, even after declaring them unacceptable, once you (re)affirm the terms as a firm, mandatory requirement. Willingness to walk away is often a strong, persuasive signal of competence and/or high demand of your service and can provoke decisions to be made more promptly by potential clients.
You can factor an intrest charge for payment delays that will encourage prompt payment, calculate by percentage and then format your payment terms to represent these differences as discounts for prompt payment instead of penalties for late payment. A secondary benifit of using these now slightly increased rates combined with prompt payment discounts is that you will be able to slightly increase your effective rate for recurring clients by adjusting these discount amounts in the event you can't or don't want to propose a higher rate. Also, IME (in the US) the initial disclosure of late payment terms or penalties may be a requirememt when including compounded interest on an outstanding debt amount in a situation where legal action to recover debt becomes necessary.