Okay, doing a bit of research, it looks like your adopted sons wil not automatically qualify for UK citizenship (as you were not living in the UK), so you will need to register them as UK citizens before you can apply for UK passports for them.
This registration can be done from the US and it costs £1,012 per child. Unfortunately, it can take up to 6 months to be processed, but you will save yourself over £6,000 in visa fees compared to doing it in the UK.
Cost of registering them as British in the US = £2,024 plus passport fees
Cost of registering them as British in the UK= about £8,500 plus passport fees (£6,000-6,500 in visa fees for them to move to the UK to start with, then £2,024 for the citizenship registration once they are living in the UK)
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