Where are the British engineers?

Throughout my career I have had the dubious pleasure of being surrounded by physicists. Some semi geniuses, some not so. Most fitting one of the character stereo types, with beards or jumpers or socks and sandals or body odour issues - some with all of them. But they all thought like physicists. So when I moved on and became surrounded by engineers, I was unfamiliar with scientists who thought differently, after all I was in agreement with Lord Rutherford  who said "All science is either physics or stamp collecting". The different mindset of physicists and engineers is something I will return to, but one difference in the scientific education of engineers has surprised me. On my degree course there were about 130  students, about 5 of them females and even fewer were overseas students. As I have visited engineering departments around the UK I have been struck by the large number of overseas students. Some engineering courses have had 90% of their students being from overseas. Dont get me wrong, I have nothing against overseas students, and universities love them because of the higher fees they pay. My concern is "where are all the British engineers?" What is it about engineering that makes British students want to do something else? And why is there seemingly no problem getting British students to study physics?
So I did what all modern people do and I googled it. There is a site that provides a breakdown of international students in UK academic institutions
 http://www.ukcisa.org.uk/about/statistics_he.php
 International students made up 14% of all first degree courses and 48% of all full time research degrees. This is not the 90% I had been told but this is across all subject areas.The breakdown with subject area is given below. It may be different for specific subjects and specific universities.

Subject of study	No of international students	% in subject who are international
Business & administrative studies	130,505	36%
Engineering & technology	51,775	32%
Social studies	38,790	17%
Creative arts & design	25,250	14%
Languages	23,270	17%
Subjects allied to medicine	23,035	8%
Computer science	21,300	22%
Law	20,810	22%
Biological sciences	19,570	10%
Physical sciences	13,025	14%
Education	11,725	6%
Architecture, building & planning	11,415	20%
Medicine & dentistry	10,605	16%
Mass communications & documentation	10,400	19%
Historical & philosophical studies	9,250	9%
Mathematical sciences	8,160	19%
Combined	2,890	3%
Agriculture & related subjects	2,415	11%
Veterinary sciences	1,025	18%
Total	435,235	17%

There is certainly concern about the number of British students getting into engineering, and rightly so. What is it about the British education system that has people heading for courses like media studies and golf course management. Well there is of course the perception that science is hard, and its not just a perception, it is hard, but it's also personally rewarding. However not so financially rewarding - unless you want to go into medicine. I do believe that governments have recognised that a lack of  UK engineers has serious consequences for a would be high tech economy, but what can they do about it? It seems to me that much of the problem is deep rooted in the British class system.  You mention an engineer and you think of someone in a boiler suit and oil covered hands. Engineering is not refined. An engineer is someone who fixes your washing machine. These stereotypes are both wrong and damaging. Engineers are highly trained, highly skilled and competent individuals. Engineers are the people who make the iphones that the golf course managers take for granted. This cultural gulf in the UK is something that will take a generation to put right once we actually start trying.
We can of course take our cue from the Germans who have engineers who understand technology running technology companies, not accountants. But that is the British way, the toffs are in charge.