First issue is the name. It sounds as if it could be too similar and so could confuse the public and creditors into thinking its oldco. In that case directors of old co (and this will be not just your partner but yourself since you say you ran oldco and thus are at risk of being considered a 'shadow director' and therefore at risk of being held to have same liabilities in law as a director) will be committing an offence if you do not come within one of the exemptions. There are only two available being either newco buys the assets and name from a liquidator/receiver/administrator of oldco (dependent on what form of insolvency solution oldco follows) and a formal notice is filed in the London Gazette, or you obtain a court order authorising the use of the new name (you must apply quickly within 7 days of the liquidation).
You have to be careful you fully buy the appropriate assets with attention given to IPR (Intellectual Property Rights) ie web domain name, website itself (the code), software, designs and images, marketing material as well as goodwill (customer/./supplier contacts) etc etc. You negotiate a fair price. IPR can sell for very little as usually there is no real market but best to ensure it properly and legally transfers in a way that is protected from challenge by a disgruntled creditor.
You need to be careful who you select as an Insolvency Practitioner to be the liquidator. Basically you agree a fixed price and he agrees to the sale a to newco and to support that to creditors in his report as a better outcome than just selling off the assets separately. Obviously these arrangements, whilst perfectly lawful, can still be open to challenge (eg over the value being paid). Your main concern is to ensure no creditor challenge. HMRC will usually be OK so long as its done properly and you use an IP not under question by HMRC previously. But you say you have one big creditor. Best to explain things to them if you have a good relationship with them. You will need their support - to vote in favour at the creditors meeting. BTW do not, as you suggest, do nothing and 'wait for a winding up order' - you need to control everything form here on to lead to a creditors voluntary liquidation not a compulsory liquidation where you will have no control) .
As to choice of IP there are big accountancy and insolvency specialist firms who charge high and individuals with lower accountancy qualification who offer low fees. In each case, but especially the latter, there are trustworthy and highly experienced individuals and others less so. I assume the business and finances are fairly straight forward so the work to be done should not be much. The more work you can do the lower the fee you can negotiate. So if you can ensure the books are up to date and simple to follow and you have a full and complete list of creditors and debtors with balances making his Report work much less time consuming, you can negotiate a lower fee.Its all about negotiating. Do not accept the first quote - get at least three and even then offer and negotiate a lower fee. They are often very commercial.
One thing you have to be careful about is whether you have a competitor who may fancy bidding for the business. Even though you pre-arrange a purchase as I set out above, the liquidator cannot ignore a higher offer.If you have a direct competitor then the business is worth more to them (because buying it kills off a competitor and may enable them to increase their prices eg if a two horse market) than to you. If one of the assets is key equipment that enables you to make the product then be careful when discussing with your major creditor since they may wish to compete for the equipment.
You need a thought out strategy not just to decide to 'launch a phoenix'. I have worked with a number of IPs and can introduce you to some to quote fees. Also happy to help with strategy but would need more detail of your business. PM if want to talk in private.