zebrax, sorry I'm unclear what you mean, you said you are not bothered about getting someone to see your dd and that it would be a hassle.
DO you mean you want to get a private SLT assessment? If so, you should contact ASLTIIP (they have a website) for a directory of private SLTS. Our department always keeps a list of local SLTs who work privately as well, it might be worth ringing them. Your HV should have a phone number for the local SLT. A private assessment costs about 80 pounds, I think.
Your child might be offered an appointment on the NHS more locally than you think, it depends what sort of area you live in (very rural?). Most departments have community clinics or outreach home visits. I'm not sure you would be expected to travel 20 miles, I could be wrong, but it wouldn't seem like an accessible service, so I would think there would be something closer.
Of course, some areas have recruitment and retetion problems, I can't say how well staffed your local area would be.
Some children have unclear speech until 3 years. It tends to even out a bit in the year prior to the fourth birthday, so if you really do have to guess what she means (and translate for other people) I'd say you might think about getting her on the waiting list for assessment. She might improve a lot between now and then, but at least you are on the list.
Ho hum, said I wouldn't post as a professional anymore....that didn't last long!