There is nothing mystical about NHS's current problems: i) fast increase in population and ii) not enough money in the coffers to fund everything that used to be funded. It is known by everyone who works in healthcare, but the public keeps getting bamboozled so that they begin to think that govt is simply depriving the service of money, but now why.
I worked in a large teaching hospital in Paddington, and as far back as 2000 the daily outpatient clinics were FULL to bursting with recently-arrived people, most requiring interpreters. That's just one speciality, and there's a knock-on effect on x-ray and other investigations which all depts need to use, as well as on admin staff who have a big increase in typing up reports and correspondence.
There is little possibility to expand in terms of more doctors taking clinics, because space is finite. You cannot tag on another consulting room, or enlarge the waiting area, or employ an extra typist because there is no space to put them. Even if NHS had the £ to run late-night OP clinics up to, say, 9pm when consulting rooms are empty in clinics, there will be an even bigger run on x-ray, phlebotomy, pharmacy, secretarial, etc.
We are recruiting nurses from overseas but insisting that our own take a uni degree in Nursing. Those nurses that do come to UK to work sometimes bring their families, or they acquire a family while living here. They become users of the NHS too. A quick glance at some areas of England and you can see that overseas nursing staff are nursing other people from overseas a lot of the time.