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Has there been any research into whether euroscepticism is a function of age or of values.

If it is a function of age then euroscepticism should (assuming constant birth/death rates) remain constant as everyone ages. But if it is a function of values, and if values are divided generationally, then we might expect a shift in eurosceptic majorities.

The majority has already shifted if polls are anything to go by (though beware, polls also suggested Remain would win), and yes, opinion on the topic very much depends on the age:

However, support and opposition for withdrawal from the EU are not evenly distributed among the different age groups: opposition to EU membership is most prevalent among those 60 and older, with a poll from 22–23 March 2015 showing that 48% of this age group oppose EU membership. This decreases to 22% among those aged 18–24 (with 56% of 18- to 24-year-olds stating that they would vote for Britain to remain in the EU).

Also, the Conservative party is in a pickle at the moment because it no longer attracts young voters. See e.g. Nick Boles, who recently resigned the Tory Whip, commenting on that on this podcast.

Yes, lots of surveys tie euroscepticism, or more precisely Leave preference to age. Here's a one with a large sample:

We use individual-level data on thousands of respondents in Understanding Society, the UK's largest household survey, which includes the EU referendum question.

We find that voting Leave is associated with older age, white ethnicity, low educational attainment, infrequent use of smartphones and the internet, receiving benefits, adverse health and low life satisfaction. These results coincide with corresponding patterns at the aggregate level of voting areas. [...]

We also show that among individuals with similar socio-economic characteristics, Labour supporters are more likely to support Remain while Conservative supporters are more likely to support Leave.

But as you noted, preferences also change with age, so one should not jump to conclusions just based on mere distribution by age now. On the other hand, not only are younger generation less eurosceptic than the elders, but they are also more pro-European than previous generations were at the corresponding age, apparently because newer cohorts are more educated. Nevertheless one should still not jump to unwarranted conclusions because other factors may play a (larger) role as well:

In the UK’s 2016 referendum on EU membership, young voters were more likely than their elders to vote Remain. Applying new methods to a half century of data, we show that this pattern reflects both ageing and cohort effects. Although voters become more Eurosceptical as they age, recent cohorts are also more pro-European than their predecessors. Much of the pro-Europeanism of these recent cohorts is accounted for by their greater years of education. Going forward, the ageing of the electorate will thus be offset at least in part by the replacement of older cohorts with younger, better-educated and more pro-European ones. But we also document large nationwide swings in sentiment that have little to do with either seasoning or cohort effects. Hence these demographic trends are unlikely to be the decisive determinants of future changes in European sentiment. Rather, nationwide changes in sentiment, reflecting macroeconomic or other conditions, and the age-turnout gradient will be key.

The big question is whether these other factors (economic etc.) will override the demographic trend.

Also, assuming Brexit happens, it's not impossible to conceive that anti-EU education may even reverse the cohort trend in long run, i.e. newer cohorts may start to be less pro-EU at the same age than the current cohort due to, say, highly nationalist education they might start to receive in schools. Even less sinister scenarios can have the same effect: emigration of the more educated to the EU because of the bad post-Brexit economic conditions in the UK. (The emigration of the young and educated is big deal in Greece for instance.)