UI-to-Code generation requires vision-language models (VLMs) to produce thousands of tokens of structured HTML/CSS from a single screenshot, making visual token efficiency critical. Existing compression methods either select tokens at inference time using task-agnostic heuristics, or zero out low-attention features without actually shortening the sequence -- neither truly reduces prefill latency or adapts to the non-uniform information density of UI screenshots. Meanwhile, optical (encoder-side learned) compression has shown strong results for document OCR, yet no prior work has adapted this paradigm to UI-to-Code generation. We propose UIPress, a lightweight learned compression module inserted between the frozen ViT encoder and the LLM decoder of Qwen3-VL-8B. UIPress combines depthwise-separable convolutions, element-guided spatial reweighting, and Transformer refinement to compress ${\sim}$6{,}700 visual tokens to a fixed budget of 256. Together with Low-Rank Adaptation (LoRA) on the decoder to bridge the representation gap, the entire system adds only ${\sim}$21.7M trainable parameters (0.26\% of the 8B base model). Under a fair comparison on the same base model against four baselines on Design2Code, UIPress at 256 tokens achieves a CLIP score of 0.8127, outperforming the uncompressed baseline by +7.5\% and the strongest inference-time method by +4.6\%, while delivering 9.1$\times$ time-to-first-token speedup. To the best of our knowledge, UIPress is the first encoder-side learned compression method for the UI-to-Code task.