Looking for a 1-2 bedroom

I am actively seeking for a 1-2 bedroom (£1250 PCM) for me and my baby boy, preferably in Northwest London or at least 40 minutes drive away from Harlesden. I will be using housing benefit to pay the rent in full as I am in receipt of Universal Credit and child benefit. Unfortunately I do not know a guarantor, which is one of the reasons why it has taken me soo long to move. I do not know anyone personally earning 3X the amount of the rent per month which is disappointing. I will be returning back to my university studies and work January 2023 so would not be relying on benefits for long. It would really help if anybody could please help me as me and my son are still at mum’s and very overcrowded + would love for him to sleep in his cot and have space to crawl and run around.

Thank you