Some people use the term 'part time' to refer to staff who are only called in on a casual basis. (i.e. with a "zero hours" contract). If that's what you're referring to, the answer to your question is 'No'.
However 'proper' part-time staff (who work regularly but for fewer hours than their full-time colleagues) are entitled to redundancy pay. Further, when considering who to select for redundancy, employers must treat part-time workers equally with full-time ones. (Employers often used to get rid of part-time workers first, without reference to such factors as length of service or work performance. That practice is now unlawful).
There's lots of information about redundancy here:
http://www.direct.gov.../Redundancy/index.htm
Chris