Hey handbaglady!
Although it’s been a while since you posted you’re message, if your still applying for doctoral study you might find these tips useful:
1.make sure the academics you’re approaching have an interest in your research area (this one’s obvious, but it leads into the next…)
2.find out what research these academics are currently working on. Have they received funding from the AHRB, the ESRC, or any other funding body for a current or forthcoming project? If they have, find out what the funding was for and see if your research interests match those of the project in any way. Could you possibly act as a research assistant to the academic?
3.basically, an academic is likely to look upon your application favourably if they clearly see that i) you have an interest in their work and ii) that you can support them in their work.
4.offer to visit the academic, this shows that you’re really interested in their work- you might want to go during a graduate open day.
5.contacting a graduate student at the department who may be familiar with the academic is a great idea.
6.try to have something not too controversial published, this suggests that your serious about academia. Though if you don’t think you have any work of publishable quality, don’t worry about it.
7.attend conferences and present papers, this is a great way to meet several academics at once, postulate your ideas and arguments, and do a great PR job in person!
This is a bit harsh but needs to be said; while some academics wont get back to you because they’re really busy, others wont get back to you because they’re not interested in your work (and they’re just too rude to mail back and let you know!), so make sure you’re not wasting your time.