The advice follows an update earlier in the week from Prime Minister, Boris Johnson, when it was announced that most COVID restrictions in England are likely to be lifted on 19 July.
Coronavirus cases have been rising sharply in recent weeks and are now on a par with the numbers recorded in mid-January.
In North Yorkshire there's been a trebling of case rates in a fortnight, from 82.4 cases a week per 100,000 people on 19 June to 261.6 cases a week on 3 July. York's case numbers have risen from 268 to 414 cases a week per 100,000 people during the same period.
'Sharp increases in infection rates'
The latest figures published on the Government's daily dashboard (correct as of 8 July) also show the highest number of cases in North Yorkshire are being recorded among people aged 20-24 (1,152.1 cases per 100,000) and those aged 15 to 19 (968.1 per 100,000).
In York, it's a similar picture with 1,364.5 cases per 100,000 among those aged 20-24 and 1,036.5 cases per 100,000 among those aged 15-19.
NHS North Yorkshire Clinical Commissioning Group Accountable Officer, Amanda Bloor, said: "The vaccination programme in North Yorkshire and York has been an incredible success story, but we're not at the finish line yet and we're now seeing sharp increases in infection rates among younger cohorts who have not had the opportunity to be fully vaccinated.
"People who haven't had both doses of the vaccine are much more susceptible to catching coronavirus than those who have been 'double-jabbed' and they should continue to exercise caution and common sense – and 'book' their COVID vaccine through the NHS national booking service, online or via 119, if they haven't already done so."
Dr Nigel Wells, a GP and Clinical Chair at NHS Vale of York CGG added: "While the vaccination programme has undoubtedly weakened the link between COVID cases and hospitalisations, we are beginning to see the early signs of a small but sustained increase in the numbers of people being admitted to our hospitals who have COVID-19."
'Stay two metres apart'
The NHS says people should continue to follow the current guidance until 19 July, when it's expected many restrictions will be removed.
At present in England, groups of up to 30 can meet outdoors and six people or two households are permitted to meet indoors (and stay overnight).
By law, face coverings must be worn on public transport and in most indoor settings, such as shops and supermarkets, and in bars and restaurants (except when seated at a table to eat or drink).
Government guidance remains that people should stay two metres apart from anyone who is not in their household or support bubble where possible, or one metre with extra precautions in place (such as wearing face coverings).
People with symptoms of COVID should self-isolate immediately if they have symptoms, have tested positive, or have been in contact with someone who has tested positive.