Yes — Benadryl (diphenhydramine) and ibuprofen work in different ways and the NHS says they can be taken together, but follow the dosing on each label and check with a pharmacist, especially before combining with cold/flu products.
They act on unrelated targets, so they are not expected to interact dangerously with each other: diphenhydramine is a sedating antihistamine that blocks histamine, while ibuprofen is an NSAID that reduces pain and inflammation by blocking prostaglandins. The NHS states plainly that you can take diphenhydramine together with painkillers such as paracetamol or ibuprofen. The catch is not the pairing itself but the products it hides in — many multi-symptom cold, flu, and "PM" sleep/pain products (for example Advil PM) already combine diphenhydramine with a painkiller, so adding a separate dose can double you up and cause an overdose.
Read every label first: do not stack two products that contain ibuprofen, and do not add diphenhydramine if your cold/flu or "PM" product already includes an antihistamine. Stay within label limits — for nonprescription ibuprofen, adults and children over 12 take a dose every 4-6 hours and no more than 6 doses in 24 hours. Treat ibuprofen's own warnings as the main risk: it can cause stomach ulcers or GI bleeding (watch for stomach pain, heartburn, vomit that is bloody or looks like coffee grounds, or blood in the stool / black tarry stools) and carries a higher heart-attack and stroke risk at high doses or long-term use — be especially careful if you have had ulcers, take a blood thinner like warfarin, or have heart, kidney, blood-pressure, or stomach problems. Do not take ibuprofen at the same time as another NSAID such as aspirin or naproxen, as that raises the risk of serious side effects like stomach bleeding. Expect extra drowsiness from diphenhydramine (worse if combined with codeine-containing or other sedating medicines) — don't drive or operate machinery until you know how it affects you, and avoid alcohol, which adds to the drowsiness. Ask a pharmacist before combining if you take other medicines or are unsure, and seek medical advice for severe or lasting symptoms.
This is general reference, not medical advice, and not a guarantee of safety. Interactions depend on your doses, health conditions, and other medicines. Always confirm with your pharmacist or doctor before combining products, and follow the dosing on each label.