I'd be surprised if your difficulty had much to do with travel agent commissions. In March of this year, most major airlines eliminated travel agent commissions &foreign/commuter airlines have since followed suit.

For some countries, a condition of entry is proof of intention to leave, most often defined as a return or onbound airline ticket. The UK isn't generally such a country for US citizens, but, for example, Australia & New Zealand are. My UK entry info says only: U.K. IMMIGRATION OFFICERS WILL DECIDE ON MAX. PERIOD OF STAY DEPENDING ON REASON FOR TRAVEL.

You can purchase an open jaw ticket, for travel into London and out of Rome. A ticket without a fixed return or changeable return is often much more expensive than a ticket with a booked return. Two one-way trips are generally more expensive than an open jaw trip. Least expensive fares are generally for shorter duration than more expensive fares.

Are you a student, or under 26? There are flexible-return fares for travelers in those categories.

Gail In Eugene but never for long