It is really, really frustrating trying to get a first (or any) job. You do unfortunately need to accept that taking on work experience staff is a complete pain for employers. It ties up and slows down staff at the company, whilst adding little immediate value: typically work experience staff achieve in a month what a full time employee achieves in a few days (otherwise they wouldn't need the experience). And if you are, for example, working in instrumentation and control who is going to take the safety responsibility for your work? You can't because you are a) not a member of staff and b) do not have the relevent experience (even if you have experience of the basic technology you will not have experience of that company's implementation).
Of course some companies will take on work experience staff, partly out of a sense of public duty and mainly becasue it can be a good way of identifying potential future staff. In my experience most work experience is found through personal contacts. There is a logical reason for this: it is unlikely that someone inside the company is going to recommend a candidate for work experience unless they think that candidate is responsible, trustworthy, genuinly interested etc. Whereas if someone writes to you cold you have no idea who they are. So you need to make as many contacts as you can. Perhaps find employers your university have worked with, or you can also try attending local IET events and try to find out in coffee break conversations if anyone konws anyone in your field.
And, however frustrating it gets, stay polite to all potential employers: given that some of them are probably reading this, calling them liars is not a good start! Remember that you are asking them do you a favour by taking a chance on you.
To be honest, at your stage you are probably better just trying to get a job rather than trying to get more experience. Don't expect to get an ideal job straight away, it may be better to get into a company at a lower level than you want and prove yourself once you're there.
And finally remember that, whatever the headlines say, there is not a shortage of engineering graduates: there is a shortage of engineering gradutes who are genuinly interested in their subject, understand that their job in a company is to help that company make money, are capable of working superbly inside a team, and have a realistic understanding of their level of knowledge. If you can demonstrate those in your CV, covering letter, and interview you should be fine.
Andy Millar CEng MIET CMgr MCMIhttp://www.linkedin.com/in/millarandy
"The aim of argument, or of discussion, should not be victory, but progress." Joseph Joubert