In the consumer market there suppliers have only two clauses they can intiate to object to a transfer.
1. There has been a continuing outstanding balance on an account for a period of 90 days or more. I.e. you owe your supplier £100.00 on your first quarter and by your 4th quester its still there if not greater.
2. there is an issue with the metering profile, meaning that either the gaining supplier hasn't correctly applied for the meter/meters (very common in older E10 or RHT set ups), or the gaining supplier does not support the meter (and associated tarrif)
In most cases an active complaint would waiver clause 1. it is also worth noting that just because they "can" object doesn't mean they "will" object. In general terms you should consider your position following a successful switch, getting away from anightmare provider is a good thing, but may leave you in a sticky situation if you now have a large balance to clear, you may not get as generous a repayment time if they do not supply you.
In your situation again speak with your supplier and find out the excact reason for the objection and if it holds very little water ensure that they remove the objection and re-apply to your supplier of choice.