BA is easier as any activity on your BA account (not only flight activity) will extend life of your account by 3 years. I'd consider
- changing earning preference on some of your hotel programs to ba miles and make a stay (almost all hotel programs will provide at least 500 ba miles for that)
- provide BA account number when renting a car (at least avis/hertz will give 500 miles for that)
- make a mileage transfer from any of your existing hotel/other accounts to BA account (i.e. for Marriott Rewards and Priority Club) you can exchange 10,000 points for 2,500 miles
- purchase something which qualify for points (see BA Executive club forum... although slim chance if you are not UK based)
- if you are in US, sign for BA signature card and get 15,000 miles with the first purchase
- if you fly BA, buy something in on-board duty free
- if you will be in UK, use travelex currency exchange, rent phone from worldroam or use BCP or BA Express parking
- subscribe for business traveler magazine (400 miles for 1 year subscription) - only as a last resort or if you really like the magazine as it is almost $180

many other options is also available