The reason for the short gap here is it is the minimum recommended gap, so it's the fastest way to ensure that you get the maximum possible coverage. In Southwark, we also have our MMR and booster very close together, to combat outbreaks of measles that have been happening since 2000. This strategy gets the population vaccination coverage to maximum the fastest.
You can delay having the booster. As people have commented, some countries wait up to 3 years. It will still be effective. It would probably be effective for a very long time after that too (see below, for information comparing a 3 month and a 4-6 year gap). But, you risk not being very immune (or even not immune at all) until the second injection. However, the chickenpox vaccine is very effective with just one dose.
We have boosters for 2 main reasons. The first is to boost, or enhance, the reaction from the first injection. The second is to make sure you are actually immune. Some vaccines only make 80-90% of people immune in any given administration, so if you have it twice, there's a up to a 99% chance of immunity. In chickenpox it does both, but mostly it is for the first reason.
In summary, definitely have the 2nd injection, even after a number of years. Ask the doctor if a third dose would be advised if it has been over 10 years since the first one.
The link and an extract... [www.cdc.gov
"persistence of antibody in children after 1 dose of single-antigen varicella vaccine was demonstrated in both short- and long-term follow-up studies. In a clinical study, the rate of antibody persistence detected by gpELISA was nearly 100% after 9 years of follow-up for 277 children (85). Another study demonstrated that although antibody titers (detected by FAMA) might decline 12--24 months after vaccination, the median titer did not change after 1--4 years and even rose after 10 years (86). In Japan, VZV antibodies were present in 37 (97%) of 38 children who received varicella vaccine 7--10 years earlier (with titers comparable to those of 29 children who had had natural varicella infection within the previous 10 years) (87) and in 100% of 25 children when followed for as long as 20 years (i.e., antibody levels were higher than those observed 10 years earlier) (88). Interpretation of long-term studies is complicated by at least two factors. First, asymptomatic boosting of vaccine-induced immunity by exposure to wild-type VZV is likely. Because varicella vaccine is not routinely recommended in Japan, coverage of children was estimated to be low (approximately 20%) during 1991--1993. Second, sample sizes were limited as a result of the decrease in the number of children followed-up with increasing time since vaccination.
The second dose of varicella vaccine in children produced an improved immunologic response that is correlated with improved protection. A comparative study of healthy children who received 1 or 2 doses of single-antigen varicella vaccine administered 3 months apart indicated that a second dose provided higher antibody levels as measured by the proportion of subjects with titers of >5 gpELISA units and by geometric mean titers (GMTs) and higher efficacy (85; Tables 2--4). The proportion of subjects with antibody titers of >5 gpELISA units in the 2-dose recipients was higher 6 weeks after the second dose than after the first dose (99.6% and 85.7%, respectively) and remained high at the end of the 9-year follow-up period, although the difference between the two regimens narrowed (97% and 95%, respectively). GMT 6 weeks after the second dose was substantially higher than that after a single dose (142 and 12, respectively). The difference in GMTs between the two regimens did not persist over 9 years of follow-up among subjects who seroconverted after vaccination, although GMTs in both regimens remained high by the end of the study period. However, receipt of a second dose decreased the rate of breakthrough varicella significantly (3.3-fold) and increased vaccine efficacy (p<0.001). Another study that assessed the immunogenicity of a second dose received 4--6 years after the first dose demonstrated a substantial increase in antibody levels in the first 7--10 days in the majority of those tested, indicating an anamnestic response. On the day of the second dose, GMT was 25.7, compared with 143.6 GMT 7--10 days after the second dose; 60% of recipients had at least a fourfold increase in antibody titers, and an additional 17% had at least a twofold increase (89). Three months after the second dose, GMT remained higher than on the day of second dose (119.0 and 25.7, respectively). Among children, VZV antibody levels and GMTs after 2 doses administered 4--6 years apart were comparable to those obtained when the 2 doses were administered 3 months apart."