Lyme disease is caused by a bacteria which is transmitted to humans through tick bites.
They also say that people in the UK are often unaware that they can catch Lyme disease and other serious infections without going overseas.
Scientists from the Liverpool School of Tropical Medicine blamed increased foreign travel and a relaxation of the quarantine laws for more exotic ticks being imported into the UK.
Those ticks bring with them diseases like encephalitis and typhus.
Lyme disease is caused by a bacteria which is transmitted to humans through tick bites.
One of the first symptoms is usually a characteristic bullseye-shaped rash.
Sufferers can also experience joint pains, fever and fatigue, and as the bacteria continues to spread around the body. Other symptoms can include a stiff neck, facial paralysis or nerve tingling.
If untreated, symptoms can worsen to include severe headaches, painful arthritis and joint swelling, heart problems and even mental disorders such as short-term memory loss and difficulty concentrating.
But if caught early, the disease is treatable with antibiotics - however, late stage Lyme disease does not respond as well.
But he said many people were oblivious of the risks and some failed to visit their GP, even though they knew they had been bitten by a tick, waiting until their condition became more serious.
Dr McGarry said: "We see a few hundred cases of Lyme disease in the UK each year, but if the GP gets to see it early then there are usually no problems.
"The false perception that native tick infestations do not represent any potential threat may be widespread.
"With the relaxation of quarantine regulations for imported dogs, the potential for the introduction and transmission of the new tick-borne diseases has increased.
"There is the potential for new diseases through infected animals."
Varying risks
Dr McGarry and his colleagues examined the records of patients transferred to their travel clinic over the last seven years and found that two-thirds of the 73 infestations originated in the UK.
Overall there were 27 ticks, 24 myiases (infestation of the skin by fly larvae; 15 ectoparasitic insects (parasites that live on the skin of their host) and seven mite infections.
Ticks predominated in the UK with 41% of cases, whereas myiasis was more common in travellers returning from abroad. Out of these only the invasive screwworm fly caused a serious infection requiring surgery.]
The study is published in The Lancet.