I've asked my GP and they won't do it, even for a fee. (It will definitely have to be done on a private basis as the chicken pox vaccine is currently not available on the NHS.)
Pumpeedo: Although complications are rare, even a small chance of complications is enough to want to vaccinate. If a childhood disease can be prevented, then it stands to reason that it should.
See evidence from the US:
Prior to the introduction of the vaccine in 1995 in the USA (released in 1988 in Japan and Korea), there were around 4,000,000 cases per year in the US, mostly children, with typically 10,500–13,000 hospital admissions (range, 8,000–18,000), and 100–150 deaths each year.[26][10] Though mostly children caught it, the majority of deaths (by as much as 80%) were among adults.
During 2003 and the first half of 2004, the US Centers for Disease Control and Prevention (CDC) reported eight deaths from varicella, six of whom were children or adolescents. These deaths and hospital admissions have substantially declined in the US due to vaccination,[27][28] though the rate of shingles infection has increased as adults are less exposed to infected children (which would otherwise help protect against shingles).[29][30][31] Ten years after the vaccine was recommended in the US, the CDC reported as much as a 90% drop in chicken pox cases, a varicella-related hospital admission decline of 71%[26] and a 97% drop in chicken pox deaths among those under 20.[32]
Also, it is not true to say that the children who are vaccinated are more susceptible to shingles. It makes un-vaccinated children more susceptible to catching shingles as adults:
www.nhs.uk/Conditions/vaccinations/Pages/chickenpox-vaccine-questions-answers.aspx
If a childhood chickenpox vaccination programme was introduced people would not catch chickenpox as children (as the infection would no longer circulate in areas where the majority of children had been vaccinated). This would leave unvaccinated children (there will always be a few who are unable or choose not to have the vaccine) susceptible to contracting chickenpox as adults when they are more likely to develop a more severe infection or a secondary complication, or in pregnancy when there is a risk of the infection harming the baby.