The Department for Education and Employment have advised that the official educational guidelines on financing a second undergraduate degree are that “previous attendance on a full-time higher education course at a publicly funded institution in the United Kingdom will usually mean that a student is not eligible for support for fees for another course. Previous attendance at a non-publicly funded institution will also usually debar them, if any support from public funds toward their fees was available to them."
Don't forget these regulations do not affect a student's eligibility for maintenance support, which includes loans and supplementary grants, provided the student meets the general eligibility criteria for such support. See Directgov's advice on Student Finance
Sources of additional support can be found on the student section of the BVA website
See the Overview and Student Finance – Resources sections of this site for trust and scholarship applications.
Studentships and fellowships are available for these courses and if you do have to pay a fee they are not as expensive.
For example, the Institute for Animal Health in Berkshire has a number of postgraduate and research initiatives. It is the largest research institute in the United Kingdom dedicated to the health of farm animals.
The Biotechnology and Biological Sciences Research Council (BBSRC) also provides such training opportunities, as do a number of universities around the UK.