You do not state how much experience you have of travel within the UK. By the time I first went abroad by myself, I was already accustomed to getting around here, and had experience of things like using timetables and maps to plan journeys, getting around by train and bus and staying at YHA hostels. I suspect planning trips abroad without that experience of domestic travel might be a bit daunting, but plentry of people do it.
If you have never gone anywhere much by yourself, consider a long trip within the UK first, where you have fewer unfamiliar things to deal with all at once. As a Londoner, you would find Scottish islands like the Orkneys or Outer Hebrides very different from your home environment, but still have everything available in English and have the NHS there if needed. Or prehaps visit Ireland, which is going abroad but without the language barrier. With that experience behind you, then you plan for going to Lisbon, Madrid and Barcelona the next year.
Re "taxis to hotels", probably not on an 18 year old's budget. I very rarely use a taxi, and I earn a good salary.
Obviously you could fly to Spain or Portugal, but I use rail and sea for that sort of journey. It 's a lot more interesting, and better for the environment.
"What if I get lost?" That is much the same at home or abroad - develop some map-reading skills here and they will transfer to doing the same elsewhere.