You are going to need a lot of research. There are many variables which need exploring which will determine your overall expenditure. First you must decide your priorities.
Which countries to stay in - each will vary considerably. e.g. European, North American, Australia, NZ, popular holiday destinations etc. will all be several times more expensive than say India, Nepal, Cambodia and such.
Pace of travel - how long to stay in each country
Mode of transport in country and between countries (fast or slow, comfort etc) The more frequently you change location, the more you spend. Plane, train, car, boat, taxi, bus, hitch, walk etc. etc.
Accommodation - again the type of accommodation, level of comfort will dictate price
Living expenses for each country - this will change between cities, towns and rural areas
Visiting tourist attractions, events, souvenirs
Socialising
Visas, local taxes, laundry, replacing shies, clothes etc.
Mobile phone charges
Upfront costs: vaccinations, travel and health insurances
Then plan contingencies and emergencies plus repatriation. Cost of living inflation is running high for everyday expenses, so bear this in mind and keep a healthy budget aside possibly as much as 20%.
£20k seems a tad light but is commensurate with the UK national living wage. By all means try to stick to this level, but have a contingency of another £10K or you will likely end up cutting your venture short.
You need to decide your priorities first.
No end of websites to help. Here's one:
https://www.earthtrekkers.com/how-much-does-it-cost-to-travel-around-the-world/