Sounds as though things are not quite so good now for graduates as they were when I graduated in the late 90's. However I can assure you that if you step into any aircraft design office you will generally see a bit of a demographic problem (lack of young staff), so there is certainly the need to recruit the youngsters in order for the UK aerospace industry to survive.
SARTOR requirements for chartership now require four years of acedemic study, ie: MEng or BEng with an MSc, alot of the large company graduate programmes are geared towards achieving chartership, hence why just a BEng may not get you onto those schemes. However getting chartered isn't actually that important, what is more you tend to learn most of what you need on the job (you do use aspects of the degree more so than in other industries), but a years experience in industry training is far more useful than an extra year at university. Infact I know plenty of stress analysts whom have only ever held a hnc or hnd.
To summarise the industry is short of engineers, P and J, your lack of experience shouldn't be too much of an issue, as a fresh graduate even if you are not on a formal training scheme, I have found in the small companies experienced engineers are generelly happy to pass on knowledge and advice. If you can follow an ESDU data sheet you should be fine.
There is a shortage of stress analysts and other specialisations, so I would expect some companies are prepared to take on graduates as trainees.