Roma in the British Isles living a traditional lifestyle (as opposed to ethnic Roma) are tiny. The Irish Republic estimates this group at around 1,000. I don't think there are UK figures but the numbers are tiny. The UK Roma have almost all settled. In the UK as in Ireland most Roma mix seasonal travel with semi-settled lifestyle - they send their children to school, work, play a part in UK society. The horse fairs are associated with this group - and yes they are a tourist attraction. The Roma have been in the British Isles for centuries and are part of British society.
Tinker populations living a traditional lifestyle are again tiny. Again this ethnic group has now almost always settled. Often there is overlap with Roma.
Roma and Tinkers who travel have sites provided by local authorities. While I'm sure the system is less than perfect, taken in the round it does seem to work. These sites are not open to New Age Travellers.
New Age Travellers are part of the settled UK population who have de-settled. They are squatters in that they live in squats, or in caravans on land which they have no right to occupy - basically shanty towns. As squatters there are immediate problems with sanitation and power for winter heating, as well as issues around whether children can be allowed to live in such conditions. The UK approach is to offer accommodation along with social security benefits so that this part of the settled UK population can re-settle.
Squats and shanty towns have no place in a civilised society. The UK policy of providing proper accommodation and benefits surely has to be right. This means that families can stay together, and treatment for drug dependency is available.