Moving from the American system into the British system is probably one of the trickiest transitions of all, and success very much depends on the age of the student and on his/her ability and willingness to adapt and take on the extra work that will undoubtedly be required. It would be exactly like jumping onto a jogging machine already going at full tilt.
It's obviously easier for students to make a reasonably seamless transition from an American school into, and back out of, an American school, but not just because the American schools are in step with the range and level of curriculum in the US and at international American schools.
American schools are also very much geared to welcoming and absorbing new students, often with a structure in place to ease them (and their parents) into school life quickly. A side benefit is that they often also take full advantage of living in a foreign city, planning classes around the museums, theatre, concerts, history, etc whenever they can.
Getting into US universities is possible from either system
US universities are familiar with GCSE and A level qualifications but, unlike the UK uni system, acceptance at a US uni is not conditional on the A level results - especially since A level exams are not even taken until several months after US letters of acceptance go out. Instead, the US universities will generally ask for GCSE's and AS level results, along with an indication of academic progress in the final (A2) year.
5 GCSE passes at grade C or higher are considered the rough equivalent of a US High School Diploma (without Honors or 'Advanced Placement' (AP) classes). This will be sufficient for a student to gain entry to less selective US colleges and universities. However, the student will have to wait until he/she is 17 years old to apply.
If a student with good GCSEs definitely intends to go to a US university, and wants to apply to more competitive universities, s/he should either complete A levels or the International Baccalaureate, or should attend an American high school that offers AP classes. The IB curriculum is especially recommended if the student might be applying to other countries for higher education (besides the US and UK). Selective US universities will have the same entry expectations as UK universities.
Changing from the American system to the British during high school
In the American system, there isn't really a mid-way marker or set of exams (like the GCSEs or IGCSEs) against which any equivalency can be set, and therefore be useful for purposes of transferring during secondary school. Only when a student has a high school diploma and transcript with AP courses, or the IB Diploma, does the next level of schooling (US or UK universities) know how to gauge course work and exams.
The concern when switching over to the National Curriculum of England is that, after 14, students in the British system begin preparing for GCSEs (national exams taken at 16, with class work very much teaching to the tests), and that's when the US system begins to differ significantly from the UK system.
After 14, it is key that a student complete an appropriate course of education: UK GCSEs, GCSE + A levels, GCSEs + US High School with AP curriculum, US High School + A level exams, or US High School Diploma depending on circumstances and educational goals. Swapping mid-course would present the student with extreme challenges.
After 16, students have already begun to specialize and concentrate on science, or maths, or literature etc. After GCSEs, they are working towards their next and final major tests - the A levels (for "advanced") in three subjects, taken when they are 17 and 18.
The best students in the best British schools do end up with a very advanced level of education in their chosen subjects, but they have been working towards that level of proficiency for several years, and graduate from high school essentially ready for graduate school (18 year olds go on to med school, law school, etc), since university is simply a sharper end of the ever narrowing (but extremely deep and thorough) educational road they've been traveling. For many students from outside that system, there may be no realistic entry point at 16, scholastically or socially.
That said, there is some anecdotal evidence suggesting that students tranferring from very strong American high schools (public and private), particularly in the northeastern US, to even the best British public schools (independent schools) have successfully made the jump and lived to tell the tale. It undoubtedly depends on the school, how well the student does on the entrance tests, how willing the new school is to support the student's adjustment, and how tough (academically, emotionally and socially) the student is.
If parents are considering sending their child back to his or her old UK school (say, a student who has missed GCSEs but wants to go back in time for A levels), the best advice from us would be for parents to start by talking to that school. The decision they will take to admit or not will be based on an assessment of how capable the students is of taking on A level in her chosen subjects. Different A levels require different degrees of preparedness and if there is a gap, some children are more capable of leaping it than others - and there is always a summer with a tutor to help.
Then, if parents need to look elsewhere, it will be a matter of having the above assessment done independently, so that they can make it easy for a school to be confident of making a success of the chosen A levels.