if you had ask this question 4 years ago , we could do a brainstorming about it but few details to keep in mind that can explain this situation

1. covid
2. inflation

So , i would suggest you to either start your skyteam trip from another european country (to reach that country/city you can find cheap flights from UK) or to override what BobTL said , suscribe to UK newsletters of skyteam airlines and wait for sales

Flexibility is your best friend , i mean sure if you target japan , a country that recently reopened borders for foreigners and is on high demand , or look for flights during high periods like december or easter , yeah its going to be expensive

if you know your destinations and dates we can suggest some ideas , otherwise only real advice is to be flexible and if skyteam is too expensive + money is main factor then go elsewhere as loyalty doesnt pay off