Honeyd,
Section 18 or 20 are both GBH offences. Do you know what the police are considering?
Section 20 is the GBH without intent and carries a possible 5 year sentence - if found guilty you may escape with a community sentence.
Section 18 is a serious offence - its GBH with intent and is on a par with murder in terms of sentence, that is, it carries a maximum life sentence. Cionviction for this is likley to land the offender in prison, especially if domestic related.
From what you say, it would be more likley that your new partner would have caused the injury rather than your slap with the handbag - nevertheless, you may be charged with a the lesser common assault which is VERY unlikley to land you in prison.
As ever with offences such as these, a good solicitor is required.