If you were in receipt of Jobseekers prior to going on to BTEA, your BTEA will stop during the summer. If you are available for and looking for full-time work, you can claim Jobseekers during the summer period. This is regardless of whether you have a baby. You will be expected to make arrangements for the care of the baby in the event that you find work.
If you are not available for full-time work during the summer due to your new family commitments, then you won't be eligible for Jobseekers. If you are parenting alone, you may be eligible for One Parent Family Payment, although that takes ages to process. You can claim Supplementary Welfare Allowance from your local Community Welfare Officer while your claim is being processed.
Your BTEA will resume in September, regardless of whether you claim Jobseekers during the summer period or not.
Have you been working as well as studying? If so, there may be an entitlement to Materntity Benefit. If so, let us know and someone will let you know of the implications.