I am also reading this with great interest Frazzled as I'm almost in the same boat.
DC1 is in L6 at the moment and we are already having the Uni talk. He is having a gap year out of necessity as he has not been in the UK for the 3 years required prior to starting at Uni. We had previously agreed that he would get a job in the gap year and could stay in our UK home and not pay board and lodgings but should save at least half his income for uni.
I have recently suggested he start looking for a summer job this year and also talked about it next year and also long term and he seemed appalled that I had suggested such a thing as it will 'interfere with his studies'.
I have already funded him through private education from the age of 4 to 13 (from 13 to 16 he was an international school which DH's company paid for) I am now funding him privately for his A levels as he HAD to go to that particular school. We've made it so clear numerous times that the financial tap turns off at the end of A levels. I have three other children to think of and the way it is now, DH and I have just had to accept that DC 3 and 4 won't be privately educated. This is very unfair as 1 and 2 who are not DH's children have been for the majority of their school years.
DS1 thinks I'm being unreasonable but I think as others have said, it is unfair if he basically gets it all and the other three won't. We can't afford it as it is and have two bills to pay by Sunday and I still don't know where all the money is going to come from.
I don't consider myself to be unreasonable to say NO, from age 18. At his age I'd been working full time for a year. My mother insisted I left school at 16 and 3 days after leaving school I was working full time and giving half my salary to my mum for housekeeping. As other posters, I worked full time and studied evenings and did it the bloody hard way.
According to DS he is going to read law at Cambridge (which from what I've read on here may be a cheaper option that other unis). Fantastic if he does it but he will have to get a job (summer one in advance as opposed to during term time) and if he needs a loan he has to get one.
So, after all this waffle (sorry!) , Frazzled, no, you are not unreasonable, you have no choice if you can't afford it and its not fair to treat your children differently.
Webwhiz and elvislives, your approach sounds very sensible.