If the goods being sold are second hand, the margin scheme in HMRC’s Notice 718 may be useful – see https://www.gov.uk/guidance/the-margin-and-global-accounting-scheme-vat-notice-718.
Otherwise, there is very little scope for VAT recovery. Being an undisclosed agent has made you an extra step in the supply chain. You can’t reclaim VAT on the £350 that your brother has paid his supplier, as that purchase was made by him rather than you. You also can’t reclaim VAT on the £600 that you’ve paid him, because he isn’t registered so hasn’t charged you VAT. All that you can reclaim VAT on is any expenses that you’ve incurred (e.g. any selling fee charged by the website), as these are services which have been supplied to you.
If you’re planning to do this again, it would be better to buy the items direct from your brother’s supplier, as this would allow you to recover the VAT.