Dividends do need to be disclosed in your personal tax returns.
As you are a basic rate taxpayer, for 2015/16 you won't have any tax to pay on your £400 dividend. For 2016/17, the first £5,000 of dividends are taxed at 0%. Look here for information on the new tax rules for dividends. You don't have to have dividend tax collected through your tax code. If you receive more than £5,000 in dividends in 2016/17, you can pay the dividend tax through your self-assessment tax return.
The partnership will need to complete a partnership tax return (SA800). All that will disclose will be the accounts figures and each partner's profit share. You should be given a copy of your partner page so that you can put your profit share into your personal tax return. There is no need for the partnership to know about your own limited company unless it conflicts with partnership agreement rules.
I hope this helps but let me know if you have any further questions.